Mendelian Randomization Report
Bidirectional and Multivariable Mendelian Randomization analysis [Obesity Traits and Hashimoto’s Thyroiditis]
Ali Taghavi Rad - Email: a.taghavirad95@@gmail.com - mob: (+98)9120912665
2024-11-26
1: Body Mass Index (BMI) on Hashimoto’s Thyroiditis (HT)
2: Waist to Hip Ratio (WHR) on Hashimoto’s Thyroiditis (HT)
3: Body Fat Percentage (BFP) on Hashimoto’s Thyroiditis (HT)
4: Waist Circumference (WC) on Hashimoto’s Thyroiditis (HT)
5: Hashimoto’s Thyroiditis (HT) on Body Mass Index (BMI)
6: Hashimoto’s Thyroiditis (HT) on Waist to Hip Ratio (WHR)
7: Hashimoto’s Thyroiditis (HT) on Body Fat Percentage (BFP)
8: Hashimoto’s Thyroiditis (HT) on Waist Circumference (WC)
- Abbreviations:
- BMI : Body Mass Index
- WHR : Waist to Hip Ratio
- BFP : Body Fat Percentage
- WC : Waist Circumference
- HT : Hashimoto’s Thyroiditis
BMI and HT
Introduction
Title: Investigating the causality between BMI on HT
- Exposure: Body Mass Index (BMI), Data downloaded from: GIANT consortium | Reference paper: Loic Yengo 2018 | GWAS ID: GCST006900
- Sample size: 456,426
- Ancestry: European
- Outcome: Hashimoto’s Thyroiditis (HT), Data downloaded from: GWAS catalog Database | Reference paper: Saori Sakaue 2021 | GWAS ID: GCST90018855
- Sample size:395,640 , Number of
cases:15,654 , Number of controls:
379,986
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 2,336,260 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 41,103 SNPs
3- Number of SNPs exposure after clumping : 521 SNPs
4- Number of total SNPs in outcome: 25,494,034 SNPs
5- Number of common variants between exposure and outcome: 498 SNPs
6- Number of SNPs after harmonization (action=2) = 498 SNPs
7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 498 SNP
8- Number of SNPs after removing those that have MAF < 0.01 = 498 SNPs
9- Checking pleiotropy by PhenoScanner:
How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 28.62 37.43 50.41 70.27 73.13 822.78How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 UBrPan E55MBv outcome exposure MR Egger 476
## 2 UBrPan E55MBv outcome exposure Weighted median 476
## 3 UBrPan E55MBv outcome exposure Inverse variance weighted 476
## 4 UBrPan E55MBv outcome exposure Simple mode 476
## 5 UBrPan E55MBv outcome exposure Weighted mode 476
## b se pval
## 1 0.5395003 0.18355992 3.452362e-03
## 2 0.3714829 0.09300390 6.489336e-05
## 3 0.3786296 0.06495165 5.562469e-09
## 4 0.3564533 0.28871708 2.175857e-01
## 5 0.3564533 0.17574059 4.308791e-02
## id.exposure id.outcome outcome exposure method Q
## 1 UBrPan E55MBv outcome exposure MR Egger 680.1400
## 2 UBrPan E55MBv outcome exposure Inverse variance weighted 681.3999
## Q_df Q_pval
## 1 474 1.464060e-09
## 2 475 1.448661e-09## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 UBrPan E55MBv outcome exposure -0.002730524 0.002914015 0.3492195
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 0.3786296 0.06495165 5.829407
## 2 beta.exposure Outlier-corrected 0.3984485 0.06039830 6.597016
## P-value
## 1 1.028232e-08
## 2 1.123628e-10
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 684.0831
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<5e-05"
##
##
## $`MR-PRESSO results`$`Outlier Test`
## RSSobs Pvalue
## 1 2.796383e-04 1
## 2 1.489174e-06 1
## 3 2.066985e-05 1
## 4 8.105638e-05 1
## 5 1.326367e-04 1
## 6 9.632280e-04 1
## 7 4.730267e-06 1
## 8 3.488989e-06 1
## 9 1.123758e-03 1
## 10 1.067400e-05 1
## 11 2.857556e-04 1
## 12 3.609349e-05 1
## 13 2.191715e-03 1
## 14 5.285834e-04 1
## 15 2.145543e-05 1
## 16 2.839974e-04 1
## 17 3.813365e-04 1
## 18 1.309635e-06 1
## 19 6.648955e-09 1
## 20 1.738580e-07 1
## 21 3.385860e-06 1
## 22 6.210678e-06 1
## 23 3.292967e-04 1
## 24 9.216664e-07 1
## 25 9.118315e-05 1
## 26 1.597723e-04 1
## 27 4.203935e-04 1
## 28 1.493027e-03 1
## 29 6.053546e-04 1
## 30 1.122578e-03 1
## 31 8.240850e-05 1
## 32 3.302038e-05 1
## 33 8.896780e-07 1
## 34 2.129866e-05 1
## 35 7.419747e-05 1
## 36 6.741651e-04 1
## 37 3.220259e-04 1
## 38 4.377896e-04 1
## 39 3.883665e-04 1
## 40 1.910371e-05 1
## 41 2.825135e-02 <0.0238
## 42 2.772963e-03 1
## 43 2.042161e-04 1
## 44 1.014392e-05 1
## 45 4.514715e-04 1
## 46 2.696560e-04 1
## 47 1.603589e-06 1
## 48 5.430788e-04 1
## 49 9.224474e-04 1
## 50 1.641257e-05 1
## 51 4.315928e-03 1
## 52 4.517612e-04 1
## 53 7.444191e-04 1
## 54 1.514205e-04 1
## 55 6.655107e-04 1
## 56 2.569637e-04 1
## 57 2.678081e-03 1
## 58 8.960256e-06 1
## 59 1.071237e-03 1
## 60 7.981169e-06 1
## 61 1.757137e-04 1
## 62 3.950715e-05 1
## 63 8.576634e-06 1
## 64 1.290167e-03 1
## 65 8.222095e-06 1
## 66 1.526780e-04 1
## 67 2.680882e-05 1
## 68 7.824235e-04 1
## 69 3.975689e-05 1
## 70 4.550837e-04 1
## 71 4.186285e-05 1
## 72 1.214443e-04 1
## 73 9.936022e-04 1
## 74 8.632447e-05 1
## 75 2.560091e-03 1
## 76 3.963423e-03 0.6188
## 77 9.827956e-05 1
## 78 9.789262e-04 1
## 79 1.261218e-04 1
## 80 1.038225e-04 1
## 81 9.619286e-05 1
## 82 2.084065e-03 1
## 83 1.268750e-04 1
## 84 2.155086e-04 1
## 85 1.994813e-05 1
## 86 3.728104e-04 1
## 87 1.143034e-03 1
## 88 5.805511e-04 1
## 89 9.320792e-04 1
## 90 2.862773e-04 1
## 91 3.153999e-04 1
## 92 1.298905e-04 1
## 93 3.087299e-04 1
## 94 1.281552e-05 1
## 95 3.366065e-04 1
## 96 2.666651e-03 1
## 97 1.407960e-04 1
## 98 9.960920e-04 1
## 99 2.772186e-05 1
## 100 1.282444e-04 1
## 101 4.894409e-04 1
## 102 5.676106e-08 1
## 103 6.241758e-04 1
## 104 7.640855e-05 1
## 105 7.980845e-04 1
## 106 2.787959e-05 1
## 107 1.920975e-03 1
## 108 8.755684e-04 1
## 109 3.419341e-04 1
## 110 3.871087e-04 1
## 111 1.672225e-03 1
## 112 1.402261e-05 1
## 113 1.029901e-04 1
## 114 3.936629e-06 1
## 115 4.188760e-04 1
## 116 1.430964e-04 1
## 117 9.968152e-05 1
## 118 4.899074e-04 1
## 119 1.511952e-02 1
## 120 1.517301e-06 1
## 121 8.481288e-05 1
## 122 2.528472e-04 1
## 123 2.308459e-04 1
## 124 3.023237e-04 1
## 125 4.065028e-04 1
## 126 1.209180e-02 1
## 127 1.837722e-04 1
## 128 2.208355e-04 1
## 129 6.707213e-05 1
## 130 2.323519e-03 1
## 131 1.618798e-04 1
## 132 7.591188e-04 1
## 133 1.612649e-05 1
## 134 2.297905e-05 1
## 135 1.394640e-04 1
## 136 5.211152e-05 1
## 137 4.403634e-06 1
## 138 2.922377e-04 1
## 139 1.967071e-05 1
## 140 1.034950e-03 1
## 141 2.157151e-03 1
## 142 8.332287e-04 1
## 143 2.359901e-03 1
## 144 1.451853e-04 1
## 145 1.164198e-07 1
## 146 1.024395e-04 1
## 147 3.388048e-04 1
## 148 8.685478e-04 1
## 149 2.531413e-03 1
## 150 1.363084e-04 1
## 151 4.852857e-05 1
## 152 1.282457e-04 1
## 153 4.272731e-04 1
## 154 3.454596e-03 1
## 155 2.303116e-05 1
## 156 7.574851e-03 1
## 157 1.579203e-05 1
## 158 1.776488e-05 1
## 159 5.787462e-05 1
## 160 3.432901e-04 1
## 161 2.733552e-04 1
## 162 1.083495e-05 1
## 163 6.896112e-04 1
## 164 3.436478e-03 1
## 165 3.230604e-03 1
## 166 5.456165e-04 1
## 167 4.356689e-04 1
## 168 2.362468e-05 1
## 169 1.201129e-05 1
## 170 1.348923e-05 1
## 171 2.504580e-04 1
## 172 4.118650e-05 1
## 173 3.577512e-05 1
## 174 7.576419e-05 1
## 175 2.700962e-03 1
## 176 8.077240e-05 1
## 177 2.862699e-04 1
## 178 8.231378e-04 1
## 179 4.952069e-03 1
## 180 1.842475e-03 1
## 181 2.440066e-05 1
## 182 1.255509e-02 1
## 183 2.913566e-04 1
## 184 8.593647e-10 1
## 185 5.027121e-05 1
## 186 4.382354e-04 1
## 187 6.775437e-07 1
## 188 5.449189e-05 1
## 189 3.028960e-03 1
## 190 2.681265e-04 1
## 191 2.239190e-04 1
## 192 2.504586e-07 1
## 193 8.321684e-04 1
## 194 1.469327e-06 1
## 195 1.503883e-04 1
## 196 5.154168e-04 1
## 197 3.269072e-05 1
## 198 3.268307e-04 1
## 199 9.160947e-05 1
## 200 9.722097e-06 1
## 201 1.572053e-03 1
## 202 4.491962e-04 1
## 203 3.722819e-05 1
## 204 1.242664e-06 1
## 205 2.774456e-05 1
## 206 3.758451e-04 1
## 207 1.025742e-04 1
## 208 1.657007e-03 1
## 209 3.687062e-03 1
## 210 1.462788e-05 1
## 211 4.924560e-03 1
## 212 1.666153e-03 1
## 213 8.091323e-05 1
## 214 2.372557e-04 1
## 215 5.026935e-05 1
## 216 3.124236e-04 1
## 217 5.705736e-06 1
## 218 3.988340e-04 1
## 219 2.454593e-04 1
## 220 4.295104e-04 1
## 221 2.361097e-04 1
## 222 3.589691e-04 1
## 223 3.844340e-05 1
## 224 2.032258e-06 1
## 225 3.574005e-03 0.238
## 226 3.388277e-09 1
## 227 4.622447e-05 1
## 228 5.492025e-06 1
## 229 2.428777e-04 1
## 230 2.079242e-04 1
## 231 4.637468e-05 1
## 232 9.395122e-04 1
## 233 8.474083e-04 1
## 234 3.847522e-05 1
## 235 1.540958e-04 1
## 236 3.511089e-06 1
## 237 9.858062e-05 1
## 238 6.302074e-05 1
## 239 1.605024e-03 1
## 240 1.348625e-04 1
## 241 8.310212e-06 1
## 242 1.454236e-03 1
## 243 1.277108e-08 1
## 244 2.550610e-04 1
## 245 1.035256e-03 1
## 246 2.446948e-03 1
## 247 1.352621e-06 1
## 248 1.867066e-04 1
## 249 7.602041e-06 1
## 250 3.492852e-05 1
## 251 1.345610e-05 1
## 252 3.418486e-04 1
## 253 3.870477e-04 1
## 254 7.869493e-05 1
## 255 8.103644e-04 1
## 256 1.727160e-03 1
## 257 8.452134e-04 1
## 258 1.133770e-04 1
## 259 3.166881e-04 1
## 260 3.827162e-04 1
## 261 3.592816e-05 1
## 262 1.378313e-03 1
## 263 5.602768e-04 1
## 264 8.382145e-04 1
## 265 4.358243e-05 1
## 266 5.864880e-05 1
## 267 8.447520e-05 1
## 268 9.209336e-05 1
## 269 2.768435e-03 1
## 270 1.316698e-03 1
## 271 8.653901e-05 1
## 272 5.094987e-06 1
## 273 6.528666e-06 1
## 274 3.104111e-04 1
## 275 4.486715e-05 1
## 276 1.513115e-04 1
## 277 1.140010e-04 1
## 278 1.165423e-05 1
## 279 1.092403e-06 1
## 280 2.894684e-04 1
## 281 1.114178e-03 1
## 282 1.139216e-05 1
## 283 5.029707e-04 1
## 284 1.595172e-05 1
## 285 1.889112e-04 1
## 286 1.003452e-05 1
## 287 1.303017e-03 1
## 288 1.456573e-03 1
## 289 6.079684e-05 1
## 290 1.252314e-03 1
## 291 8.645404e-05 1
## 292 5.163470e-05 1
## 293 1.216488e-05 1
## 294 5.875313e-05 1
## 295 3.997211e-04 1
## 296 1.674088e-04 1
## 297 1.659845e-03 1
## 298 1.105267e-03 1
## 299 2.815127e-05 1
## 300 5.652023e-04 1
## 301 1.793056e-05 1
## 302 2.938122e-07 1
## 303 4.823439e-04 1
## 304 1.824802e-03 1
## 305 3.395994e-05 1
## 306 2.039536e-04 1
## 307 9.979030e-05 1
## 308 7.525440e-05 1
## 309 2.174455e-04 1
## 310 7.983056e-04 1
## 311 6.048218e-05 1
## 312 8.427636e-06 1
## 313 3.153642e-04 1
## 314 3.238131e-04 1
## 315 1.332963e-04 1
## 316 4.516050e-04 1
## 317 1.782074e-05 1
## 318 8.945019e-05 1
## 319 1.712648e-04 1
## 320 1.241963e-03 1
## 321 1.895589e-04 1
## 322 1.079876e-03 1
## 323 1.400956e-04 1
## 324 5.168689e-08 1
## 325 1.290098e-04 1
## 326 3.108573e-05 1
## 327 1.324065e-04 1
## 328 5.014255e-04 1
## 329 8.515350e-06 1
## 330 2.609272e-06 1
## 331 3.991955e-04 1
## 332 5.681275e-04 1
## 333 1.277278e-05 1
## 334 6.820517e-04 1
## 335 2.761757e-05 1
## 336 1.898249e-06 1
## 337 1.191397e-04 1
## 338 1.031368e-05 1
## 339 2.470100e-07 1
## 340 1.242537e-04 1
## 341 4.889170e-04 1
## 342 6.602620e-04 1
## 343 1.445644e-05 1
## 344 5.927086e-04 1
## 345 1.144314e-03 1
## 346 4.601322e-04 1
## 347 9.266793e-04 1
## 348 6.821474e-04 1
## 349 7.299964e-04 1
## 350 4.553018e-06 1
## 351 2.529051e-06 1
## 352 2.983745e-07 1
## 353 4.989044e-04 1
## 354 6.797941e-05 1
## 355 6.305818e-10 1
## 356 6.084800e-06 1
## 357 4.988601e-04 1
## 358 7.004599e-04 1
## 359 3.866450e-04 1
## 360 1.067716e-03 1
## 361 4.951778e-04 1
## 362 9.645922e-04 1
## 363 1.136097e-04 1
## 364 6.283289e-05 1
## 365 4.949462e-05 1
## 366 2.843307e-04 1
## 367 1.615652e-04 1
## 368 1.831699e-04 1
## 369 1.832919e-05 1
## 370 1.730347e-04 1
## 371 3.260090e-04 1
## 372 2.536805e-04 1
## 373 1.663605e-03 1
## 374 3.053509e-05 1
## 375 3.397729e-04 1
## 376 6.292764e-04 1
## 377 3.814856e-04 1
## 378 4.005317e-04 1
## 379 2.140680e-03 1
## 380 4.418214e-04 1
## 381 7.274149e-05 1
## 382 1.659496e-03 1
## 383 3.955939e-04 1
## 384 2.068869e-03 1
## 385 2.368938e-04 1
## 386 3.781707e-03 1
## 387 3.466624e-05 1
## 388 3.613337e-04 1
## 389 1.306404e-04 1
## 390 1.586323e-04 1
## 391 1.570922e-05 1
## 392 8.160825e-04 1
## 393 2.781586e-03 0.952
## 394 1.315443e-04 1
## 395 3.957981e-05 1
## 396 6.309801e-04 1
## 397 6.384784e-06 1
## 398 5.450129e-04 1
## 399 1.314197e-03 1
## 400 1.123578e-05 1
## 401 1.220448e-03 1
## 402 1.223561e-03 1
## 403 4.697977e-04 1
## 404 3.971923e-04 1
## 405 4.975426e-07 1
## 406 1.959227e-04 1
## 407 4.672102e-04 1
## 408 1.750205e-04 1
## 409 1.467171e-03 1
## 410 2.664352e-08 1
## 411 7.029796e-06 1
## 412 1.224205e-04 1
## 413 8.794988e-06 1
## 414 2.563991e-05 1
## 415 2.256944e-04 1
## 416 3.248363e-04 1
## 417 7.541194e-05 1
## 418 1.927604e-04 1
## 419 1.011615e-04 1
## 420 4.919029e-05 1
## 421 2.070326e-03 1
## 422 9.466296e-04 1
## 423 1.150006e-04 1
## 424 1.154084e-06 1
## 425 1.281693e-03 1
## 426 1.296385e-05 1
## 427 7.379213e-04 1
## 428 1.491283e-03 1
## 429 3.471925e-04 1
## 430 1.165955e-03 1
## 431 1.733419e-05 1
## 432 2.968002e-04 1
## 433 4.962012e-04 1
## 434 3.501282e-05 1
## 435 1.331322e-04 1
## 436 4.373613e-06 1
## 437 4.269002e-04 1
## 438 9.238118e-05 1
## 439 4.077510e-05 1
## 440 6.739249e-05 1
## 441 2.386615e-04 1
## 442 1.768074e-04 1
## 443 1.515879e-04 1
## 444 1.042794e-04 1
## 445 7.924022e-04 1
## 446 3.050757e-04 1
## 447 2.952526e-04 1
## 448 9.838176e-04 1
## 449 3.232214e-03 1
## 450 8.850905e-04 1
## 451 2.413713e-04 1
## 452 1.312631e-04 1
## 453 3.512845e-04 1
## 454 4.375021e-04 1
## 455 2.552891e-05 1
## 456 3.147171e-04 1
## 457 1.181185e-04 1
## 458 3.953392e-04 1
## 459 3.650037e-04 1
## 460 1.788308e-03 1
## 461 7.320751e-04 1
## 462 3.379189e-05 1
## 463 1.866409e-04 1
## 464 2.580680e-03 1
## 465 2.165064e-03 1
## 466 5.412996e-04 1
## 467 3.076925e-04 1
## 468 1.935394e-04 1
## 469 1.395207e-04 1
## 470 2.062803e-05 1
## 471 8.302662e-06 1
## 472 3.316757e-06 1
## 473 1.156781e-05 1
## 474 1.427934e-05 1
## 475 5.908579e-05 1
## 476 3.351450e-04 1
##
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 41
##
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure
## -4.974029
##
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.7523## id.exposure id.outcome outcome exposure method nsnp
## 1 UBrPan E55MBv outcome exposure MR Egger 475
## 2 UBrPan E55MBv outcome exposure Weighted median 475
## 3 UBrPan E55MBv outcome exposure Inverse variance weighted 475
## 4 UBrPan E55MBv outcome exposure Simple mode 475
## 5 UBrPan E55MBv outcome exposure Weighted mode 475
## b se pval
## 1 0.5020618 0.17070766 3.431273e-03
## 2 0.3715559 0.09204898 5.425396e-05
## 3 0.3984485 0.06039830 4.195144e-11
## 4 0.3442747 0.26847127 2.003459e-01
## 5 0.3727984 0.17083094 2.958021e-02
## id.exposure id.outcome outcome exposure method Q
## 1 UBrPan E55MBv outcome exposure MR Egger 586.6165
## 2 UBrPan E55MBv outcome exposure Inverse variance weighted 587.1389
## Q_df Q_pval
## 1 473 0.0002750681
## 2 474 0.0002925237## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 UBrPan E55MBv outcome exposure -0.001759702 0.002711426 0.5166566
Studentized residuals:
Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 0.3984362 0.06039754 6.596895 4.198580e-11
## Iterative 0.3984362 0.06039754 6.596895 4.198580e-11
## Exact (FE) 0.4060776 0.05431601 7.476204 7.650038e-14
## Exact (RE) 0.4046144 0.05949561 6.800744 3.145262e-11
##
##
## Residual standard error: 1.112 on 474 degrees of freedom
##
## F-statistic: 43.52 on 1 and 474 DF, p-value: 1.12e-10
## Q-Statistic for heterogeneity: 586.1241 on 474 DF , p-value: 0.0003250176
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points.
It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.
## 41 63 74 81 88 118 125
## 0.01460871 0.01753910 0.01087195 0.01429283 0.01456123 0.40736232 0.06002126
## 142 153 155 163 178 181 188
## 0.01467411 0.01443601 0.12452966 0.06141379 0.01328626 0.03837115 0.01479485
## 208 210 245 297 385 401 463
## 0.01362507 0.07437085 0.01804562 0.01440249 0.19920267 0.01083294 0.01651874Run After deleting new outlier: Final Results:
## id.exposure id.outcome outcome exposure method nsnp
## 1 UBrPan E55MBv outcome exposure MR Egger 445
## 2 UBrPan E55MBv outcome exposure Weighted median 445
## 3 UBrPan E55MBv outcome exposure Inverse variance weighted 445
## 4 UBrPan E55MBv outcome exposure Simple mode 445
## 5 UBrPan E55MBv outcome exposure Weighted mode 445
## b se pval
## 1 0.5220657 0.17100707 2.402946e-03
## 2 0.4042090 0.09318230 1.438959e-05
## 3 0.4225579 0.05777038 2.584608e-13
## 4 0.3806087 0.25202401 1.317017e-01
## 5 0.4088583 0.17553562 2.029603e-02
## id.exposure id.outcome outcome exposure method Q
## 1 UBrPan E55MBv outcome exposure MR Egger 421.2740
## 2 UBrPan E55MBv outcome exposure Inverse variance weighted 421.6562
## Q_df Q_pval
## 1 443 0.7641431
## 2 444 0.7704410## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 UBrPan E55MBv outcome exposure -0.001631038 0.002638196 0.5367348
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 UBrPan E55MBv outcome exposure MR Egger 445
## 2 UBrPan E55MBv outcome exposure Weighted median 445
## 3 UBrPan E55MBv outcome exposure Inverse variance weighted 445
## 4 UBrPan E55MBv outcome exposure Simple mode 445
## 5 UBrPan E55MBv outcome exposure Weighted mode 445
## b se pval lo_ci up_ci or or_lci95
## 1 0.5220657 0.17100707 2.402946e-03 0.18689185 0.8572396 1.685506 1.2054969
## 2 0.4042090 0.08759939 3.944404e-06 0.23251423 0.5759038 1.498117 1.2617684
## 3 0.4225579 0.05777038 2.584608e-13 0.30932791 0.5357878 1.525859 1.3625091
## 4 0.3806087 0.25388130 1.345428e-01 -0.11699869 0.8782160 1.463175 0.8895864
## 5 0.4088583 0.16499005 1.358001e-02 0.08547778 0.7322388 1.505098 1.0892374
## or_uci95
## 1 2.356646
## 2 1.778737
## 3 1.708794
## 4 2.406602
## 5 2.079731Sensitivity analyses with MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 445
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.423 0.058 0.309, 0.536 0.000
## ------------------------------------------------------------------
## Residual standard error = 0.975
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 421.6562 on 444 degrees of freedom, (p-value = 0.7704). I^2 = 0.0%.
## F statistic = 67.3.## Method Estimate Std Error 95% CI P-value
## Simple median 0.372 0.085 0.205 0.539 0.000
## Weighted median 0.407 0.091 0.229 0.584 0.000
## Penalized weighted median 0.396 0.091 0.218 0.573 0.000
##
## IVW 0.423 0.058 0.309 0.536 0.000
## Penalized IVW 0.413 0.058 0.300 0.527 0.000
## Robust IVW 0.400 0.053 0.297 0.503 0.000
## Penalized robust IVW 0.399 0.052 0.297 0.501 0.000
##
## MR-Egger 0.522 0.171 0.187 0.857 0.002
## (intercept) -0.002 0.003 -0.007 0.004 0.536
## Penalized MR-Egger 0.520 0.171 0.184 0.856 0.002
## (intercept) -0.002 0.003 -0.007 0.003 0.521
## Robust MR-Egger 0.515 0.131 0.259 0.771 0.000
## (intercept) -0.002 0.002 -0.006 0.003 0.403
## Penalized robust MR-Egger 0.515 0.129 0.261 0.769 0.000
## (intercept) -0.002 0.002 -0.006 0.003 0.394
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| UBrPan | E55MBv | exposure | outcome | 0.065265 | 0.0012016 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
Working with MRraps
## $beta.hat
## [1] 0.4288058
##
## $beta.se
## [1] 0.05874331
##
## $beta.p.value
## [1] 2.884359e-13
##
## $naive.se
## [1] 0.05829219
##
## $chi.sq.test
## [1] 420.8623## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 0.4288058 0.05874331
## 2 FALSE huber 0.4084349 0.06025851
## 3 FALSE tukey 0.4067305 0.06025774
## 4 TRUE l2 0.4288054 0.05874593
## 5 TRUE huber 0.4084349 0.06026027
## 6 TRUE tukey 0.4067305 0.06025955##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 445
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.428 0.058 0.000 [0.314,0.542]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 445
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.429 0.059 0.314, 0.544 0.000 1398.109
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 445
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.409 0.194 0.028, 0.789 0.035
## ------------------------------------------------------------------
WHR and HT
Introduction
Title: Investigating the causality between WHR on HT
- Exposure: Waist to Hip Ratio (WHR), Data downloaded from: GIANT consortium | Reference paper: Dmitry Shungin 2015 | GWAS ID: GCST004064
- Sample size:142,762
- Ancestry: European
- Outcome: Hashimoto’s Thyroiditis (HT), Data downloaded from: GWAS catalog Database | Reference paper: Saori Sakaue 2021 | GWAS ID: GCST90018855
- Sample size:395,640 , Number of
cases:15,654 , Number of controls:
379,986
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 2,560,781 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 544 SNPs
3- Number of SNPs exposure after clumping : 29 SNPs
4- Number of total SNPs in outcome: 25,660,792 SNPs
5- Number of common variants between exposure and outcome: 29 SNPs
7- Number of SNPs after harmonization (action=2) = 26 SNPs
8- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 26 SNP
9- Number of SNPs after removing those that have MAF < 0.01 = 26 SNPs
10- Checking pleiotropy by PhenoScanner:
How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 31.47 33.15 38.61 44.94 46.52 169.79How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 N6sC8E lSRCpg outcome exposure MR Egger 26
## 2 N6sC8E lSRCpg outcome exposure Weighted median 26
## 3 N6sC8E lSRCpg outcome exposure Inverse variance weighted 26
## 4 N6sC8E lSRCpg outcome exposure Simple mode 26
## 5 N6sC8E lSRCpg outcome exposure Weighted mode 26
## b se pval
## 1 0.40677524 0.8481933 0.6358686
## 2 0.27930499 0.2227768 0.2099353
## 3 0.07395743 0.1832071 0.6864466
## 4 0.30551025 0.4494672 0.5029298
## 5 0.46986960 0.3368696 0.1753433
## id.exposure id.outcome outcome exposure method Q
## 1 N6sC8E lSRCpg outcome exposure MR Egger 39.56586
## 2 N6sC8E lSRCpg outcome exposure Inverse variance weighted 39.83256
## Q_df Q_pval
## 1 24 0.02379768
## 2 25 0.03034011## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 N6sC8E lSRCpg outcome exposure -0.008596036 0.02137188 0.6910874
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat P-value
## 1 beta.exposure Raw 0.07395743 0.1832071 0.403682 0.6898788
## 2 beta.exposure Outlier-corrected NA NA NA NA
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 43.1747
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.0342
##
##
## $`MR-PRESSO results`$`Outlier Test`
## RSSobs Pvalue
## 1 9.493405e-09 1
## 2 1.897269e-03 0.4654
## 3 2.282802e-04 1
## 4 3.106932e-04 1
## 5 9.146917e-04 1
## 6 2.197246e-05 1
## 7 7.228149e-04 1
## 8 1.813512e-02 0.65
## 9 3.536541e-04 1
## 10 1.120301e-03 1
## 11 9.809659e-06 1
## 12 1.096665e-05 1
## 13 5.058903e-04 1
## 14 6.807367e-04 1
## 15 2.049507e-05 1
## 16 2.756644e-04 1
## 17 1.499848e-03 0.5486
## 18 5.610585e-05 1
## 19 5.921551e-04 1
## 20 3.796675e-03 0.1534
## 21 1.599047e-05 1
## 22 2.969934e-04 1
## 23 7.460494e-05 1
## 24 6.198409e-04 1
## 25 1.409228e-04 1
## 26 1.157995e-04 1
##
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] "No significant outliers"
##
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## [1] NA
##
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] NARadial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 0.07395058 0.1832105 0.4036372 0.6864795
## Iterative 0.07395058 0.1832105 0.4036372 0.6864795
## Exact (FE) 0.07623916 0.1451601 0.5252076 0.5994389
## Exact (RE) 0.07537927 0.1832045 0.4114488 0.6842495
##
##
## Residual standard error: 1.262 on 25 degrees of freedom
##
## F-statistic: 0.16 on 1 and 25 DF, p-value: 0.69
## Q-Statistic for heterogeneity: 39.82473 on 25 DF , p-value: 0.0303961
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points.
It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.
## 8
## 1.362547## [1] 8Run After deleting new outlier: Final Results:
## id.exposure id.outcome outcome exposure method nsnp
## 1 N6sC8E lSRCpg outcome exposure MR Egger 13
## 2 N6sC8E lSRCpg outcome exposure Weighted median 13
## 3 N6sC8E lSRCpg outcome exposure Inverse variance weighted 13
## 4 N6sC8E lSRCpg outcome exposure Simple mode 13
## 5 N6sC8E lSRCpg outcome exposure Weighted mode 13
## b se pval
## 1 0.6201107 0.7591858 0.431371669
## 2 0.6668341 0.2570087 0.009470191
## 3 0.5840293 0.1934547 0.002536552
## 4 0.6274265 0.3864626 0.130439846
## 5 0.6779754 0.3428469 0.071416716
## id.exposure id.outcome outcome exposure method Q
## 1 N6sC8E lSRCpg outcome exposure MR Egger 3.287914
## 2 N6sC8E lSRCpg outcome exposure Inverse variance weighted 3.290330
## Q_df Q_pval
## 1 11 0.9863476
## 2 12 0.9931240## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 N6sC8E lSRCpg outcome exposure -0.0009507916 0.01934515 0.9616817
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 N6sC8E lSRCpg outcome exposure MR Egger 13
## 2 N6sC8E lSRCpg outcome exposure Weighted median 13
## 3 N6sC8E lSRCpg outcome exposure Inverse variance weighted 13
## 4 N6sC8E lSRCpg outcome exposure Simple mode 13
## 5 N6sC8E lSRCpg outcome exposure Weighted mode 13
## b se pval lo_ci up_ci or or_lci95
## 1 0.6201107 0.7591858 0.431371669 -0.86789348 2.1081149 1.859134 0.4198350
## 2 0.6668341 0.2722169 0.014299797 0.13328904 1.2003791 1.948060 1.1425802
## 3 0.5840293 0.1934547 0.002536552 0.20485817 0.9632005 1.793250 1.2273510
## 4 0.6274265 0.4070253 0.149144019 -0.17034320 1.4251961 1.872785 0.8433753
## 5 0.6779754 0.3345107 0.065500184 0.02233442 1.3336164 1.969885 1.0225857
## or_uci95
## 1 8.232707
## 2 3.321376
## 3 2.620069
## 4 4.158673
## 5 3.794742Sensitivity analyses with MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 13
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.584 0.193 0.205, 0.963 0.003
## ------------------------------------------------------------------
## Residual standard error = 0.524
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 3.2903 on 12 degrees of freedom, (p-value = 0.9931). I^2 = 0.0%.
## F statistic = 50.1.## Method Estimate Std Error 95% CI P-value
## Simple median 0.650 0.266 0.129 1.171 0.014
## Weighted median 0.668 0.260 0.157 1.178 0.010
## Penalized weighted median 0.668 0.260 0.157 1.178 0.010
##
## IVW 0.584 0.193 0.205 0.963 0.003
## Penalized IVW 0.584 0.193 0.205 0.963 0.003
## Robust IVW 0.601 0.179 0.250 0.951 0.001
## Penalized robust IVW 0.601 0.179 0.250 0.951 0.001
##
## MR-Egger 0.620 0.759 -0.868 2.108 0.414
## (intercept) -0.001 0.019 -0.039 0.037 0.961
## Penalized MR-Egger 0.620 0.759 -0.868 2.108 0.414
## (intercept) -0.001 0.019 -0.039 0.037 0.961
## Robust MR-Egger 0.704 0.508 -0.291 1.699 0.166
## (intercept) -0.003 0.013 -0.028 0.022 0.833
## Penalized robust MR-Egger 0.704 0.508 -0.291 1.699 0.166
## (intercept) -0.003 0.013 -0.028 0.022 0.833
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| N6sC8E | lSRCpg | exposure | outcome | 0.0045076 | 3.14e-05 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
Working with MRraps
## $beta.hat
## [1] 0.5879963
##
## $beta.se
## [1] 0.2004967
##
## $beta.p.value
## [1] 0.003360302
##
## $naive.se
## [1] 0.1984777
##
## $chi.sq.test
## [1] 3.238489## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 0.5879963 0.2004967
## 2 FALSE huber 0.5879963 0.2057051
## 3 FALSE tukey 0.5930146 0.2057561
## 4 TRUE l2 0.5879964 0.2005585
## 5 TRUE huber 0.5879963 0.2057687
## 6 TRUE tukey 0.5930146 0.2058231##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 13
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.588 0.196 0.003 [0.204,0.972]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 13
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.596 0.199 0.206, 0.986 0.003 176.931
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 13
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.678 0.376 -0.059, 1.415 0.072
## ------------------------------------------------------------------
BFP and HT
Introduction
Title: Investigating the causality between BFP on HT
- Exposure: Body Fit Percentage (BFP), Data downloaded from: Open GWAS | Reference paper: Body fat percentage 2018 | GWAS ID: ukb-b-8909
- Sample size:454,633
- Ancestry: European
- Outcome: Hashimoto’s Thyroiditis (HT), Data downloaded from: GWAS catalog Database | Reference paper: Saori Sakaue 2021 | GWAS ID: GCST90018855
- Sample size:395,640 , Number of
cases:15,654 , Number of controls:
379,986
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 9,837,128 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 50,635 SNPs
3- Number of SNPs exposure after clumping : 395 SNPs
4- Number of total SNPs in outcome: 25,494,034 SNPs
5- Number of common variants between exposure and outcome: 370 SNPs
7- Number of SNPs after harmonization (action=2) = 354 SNPs
8- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 354 SNP
9- Number of SNPs after removing those that have MAF < 0.01 = 354 SNPs
10- Checking pleiotropy by PhenoScanner:
How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 29.73 36.10 43.88 57.85 59.72 681.93How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 36OsIE wtLUTb outcome exposure MR Egger 353
## 2 36OsIE wtLUTb outcome exposure Weighted median 353
## 3 36OsIE wtLUTb outcome exposure Inverse variance weighted 353
## 4 36OsIE wtLUTb outcome exposure Simple mode 353
## 5 36OsIE wtLUTb outcome exposure Weighted mode 353
## b se pval
## 1 -0.38507538 0.28537742 1.780928e-01
## 2 -0.45651283 0.12592743 2.887316e-04
## 3 -0.40325081 0.08844356 5.129653e-06
## 4 0.08978292 0.39322296 8.195256e-01
## 5 -0.65985411 0.30147982 2.927392e-02
## id.exposure id.outcome outcome exposure method Q
## 1 36OsIE wtLUTb outcome exposure MR Egger 476.1866
## 2 36OsIE wtLUTb outcome exposure Inverse variance weighted 476.1927
## Q_df Q_pval
## 1 351 9.276022e-06
## 2 352 1.088141e-05## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 36OsIE wtLUTb outcome exposure -0.0002574515 0.003842707 0.9466219
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw -0.4034657 0.0884239 -4.562857
## 2 beta.exposure Outlier-corrected NA NA NA
## P-value
## 1 6.974094e-06
## 2 NA
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 480.0678
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<4e-05"
##
##
## $`MR-PRESSO results`$`Outlier Test`
## RSSobs Pvalue
## 1 5.385832e-04 1
## 2 1.238476e-05 1
## 3 6.901517e-08 1
## 4 4.574568e-04 1
## 5 1.494669e-04 1
## 6 1.062879e-04 1
## 7 1.620091e-03 1
## 8 2.067088e-06 1
## 9 4.280177e-05 1
## 10 3.177953e-04 1
## 11 3.656414e-04 1
## 12 2.151977e-07 1
## 13 1.888113e-04 1
## 14 1.228239e-04 1
## 15 2.725863e-04 1
## 16 2.089499e-04 1
## 17 2.568255e-04 1
## 18 6.317205e-04 1
## 19 1.712762e-04 1
## 20 1.695643e-03 1
## 21 2.084410e-03 1
## 22 8.150654e-04 1
## 23 7.911814e-03 0.24072
## 24 2.608066e-05 1
## 25 1.474283e-04 1
## 26 2.097534e-03 1
## 27 1.177388e-04 1
## 28 6.044905e-05 1
## 29 1.250022e-03 1
## 30 1.884516e-04 1
## 31 2.141546e-04 1
## 32 2.781019e-04 1
## 33 2.809919e-04 1
## 34 4.586872e-04 1
## 35 1.317085e-04 1
## 36 3.877761e-04 1
## 37 8.714569e-05 1
## 38 4.657732e-03 0.65136
## 39 4.774082e-05 1
## 40 1.988448e-05 1
## 41 3.736142e-03 1
## 42 1.056856e-02 1
## 43 2.507428e-04 1
## 44 1.013546e-03 1
## 45 5.052449e-04 1
## 46 4.401590e-04 1
## 47 3.133794e-03 0.36816
## 48 1.918377e-03 1
## 49 3.624169e-04 1
## 50 8.132548e-04 1
## 51 9.455878e-04 1
## 52 4.784133e-05 1
## 53 1.551978e-04 1
## 54 4.609154e-04 1
## 55 2.174238e-05 1
## 56 7.930030e-07 1
## 57 8.488609e-04 1
## 58 1.457717e-03 1
## 59 3.635529e-03 1
## 60 3.396076e-04 1
## 61 6.977933e-04 1
## 62 1.481503e-04 1
## 63 7.210685e-04 1
## 64 6.605221e-03 1
## 65 1.139116e-03 1
## 66 3.877390e-05 1
## 67 1.368147e-03 1
## 68 6.896902e-05 1
## 69 9.304876e-05 1
## 70 3.901379e-04 1
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## 350 1.092376e-03 1
## 351 1.370136e-03 1
## 352 1.367958e-04 1
## 353 3.835279e-03 0.09912
## 354 6.012350e-05 1
##
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] "No significant outliers"
##
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## [1] NA
##
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] NARadial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) -0.4034325 0.08842763 -4.562290 5.059867e-06
## Iterative -0.4034325 0.08842763 -4.562290 5.059867e-06
## Exact (FE) -0.4129634 0.07609809 -5.426725 5.739749e-08
## Exact (RE) -0.4104574 0.08659467 -4.739984 3.104691e-06
##
##
## Residual standard error: 1.162 on 353 degrees of freedom
##
## F-statistic: 20.81 on 1 and 353 DF, p-value: 6.99e-06
## Q-Statistic for heterogeneity: 476.6866 on 353 DF , p-value: 1.192346e-05
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points.
It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.
## 41 42 59 64 80 83 108
## 0.01990057 0.04748505 0.03529283 0.03339141 0.07589678 0.15680098 0.10893105
## 139 182 225 241 247 280 287
## 0.02548446 0.04794978 0.47130068 0.09831783 0.01744461 0.05158769 0.14978191
## 327
## 0.10494023## [1] 23 42 64 80 83 99 120 139 182 213 225 241 280 287 298 327Run After deleting new outlier: Final Results:
## id.exposure id.outcome outcome exposure method nsnp
## 1 36OsIE wtLUTb outcome exposure MR Egger 318
## 2 36OsIE wtLUTb outcome exposure Weighted median 318
## 3 36OsIE wtLUTb outcome exposure Inverse variance weighted 318
## 4 36OsIE wtLUTb outcome exposure Simple mode 318
## 5 36OsIE wtLUTb outcome exposure Weighted mode 318
## b se pval
## 1 -0.58585178 0.32202357 6.981461e-02
## 2 -0.44999521 0.13013533 5.443995e-04
## 3 -0.48269876 0.08464925 1.181743e-08
## 4 -0.01000789 0.38896443 9.794892e-01
## 5 -0.54229425 0.29714007 6.893505e-02
## id.exposure id.outcome outcome exposure method Q
## 1 36OsIE wtLUTb outcome exposure MR Egger 283.0949
## 2 36OsIE wtLUTb outcome exposure Inverse variance weighted 283.2051
## Q_df Q_pval
## 1 316 0.9083303
## 2 317 0.9140844## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 36OsIE wtLUTb outcome exposure 0.001363986 0.004108351 0.7401068
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 36OsIE wtLUTb outcome exposure MR Egger 318
## 2 36OsIE wtLUTb outcome exposure Weighted median 318
## 3 36OsIE wtLUTb outcome exposure Inverse variance weighted 318
## 4 36OsIE wtLUTb outcome exposure Simple mode 318
## 5 36OsIE wtLUTb outcome exposure Weighted mode 318
## b se pval lo_ci up_ci or
## 1 -0.58585178 0.32202357 6.981461e-02 -1.2170180 0.04531442 0.5566315
## 2 -0.44999521 0.12136949 2.091942e-04 -0.6878794 -0.21211100 0.6376312
## 3 -0.48269876 0.08464925 1.181743e-08 -0.6486113 -0.31678622 0.6171157
## 4 -0.01000789 0.38788728 9.794323e-01 -0.7702670 0.75025118 0.9900420
## 5 -0.54229425 0.30926717 8.048587e-02 -1.1484579 0.06386940 0.5814128
## or_lci95 or_uci95
## 1 0.2961119 1.0463568
## 2 0.5026408 0.8088749
## 3 0.5227713 0.7284865
## 4 0.4628895 2.1175318
## 5 0.3171254 1.0659532Sensitivity analyses with MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 319
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW -0.483 0.085 -0.649, -0.317 0.000
## ------------------------------------------------------------------
## Residual standard error = 0.946
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 284.3431 on 318 degrees of freedom, (p-value = 0.9128). I^2 = 0.0%.
## F statistic = 52.8.## Method Estimate Std Error 95% CI P-value
## Simple median -0.428 0.126 -0.674 -0.181 0.001
## Weighted median -0.462 0.126 -0.709 -0.214 0.000
## Penalized weighted median -0.462 0.126 -0.710 -0.215 0.000
##
## IVW -0.483 0.085 -0.649 -0.317 0.000
## Penalized IVW -0.483 0.085 -0.649 -0.317 0.000
## Robust IVW -0.480 0.078 -0.634 -0.326 0.000
## Penalized robust IVW -0.480 0.078 -0.634 -0.326 0.000
##
## MR-Egger -0.585 0.322 -1.216 0.047 0.069
## (intercept) 0.001 0.004 -0.007 0.009 0.744
## Penalized MR-Egger -0.585 0.322 -1.216 0.047 0.069
## (intercept) 0.001 0.004 -0.007 0.009 0.744
## Robust MR-Egger -0.627 0.249 -1.115 -0.138 0.012
## (intercept) 0.002 0.003 -0.005 0.009 0.574
## Penalized robust MR-Egger -0.627 0.249 -1.115 -0.138 0.012
## (intercept) 0.002 0.003 -0.005 0.009 0.574
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| 36OsIE | wtLUTb | exposure | outcome | 0.0370296 | 0.0008009 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
Working with MRraps
## $beta.hat
## [1] -0.4911237
##
## $beta.se
## [1] 0.08648412
##
## $beta.p.value
## [1] 1.356642e-08
##
## $naive.se
## [1] 0.08565622
##
## $chi.sq.test
## [1] 283.7915## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 -0.4911237 0.08648412
## 2 FALSE huber -0.4865283 0.08872731
## 3 FALSE tukey -0.4882809 0.08872879
## 4 TRUE l2 -0.4911235 0.08648876
## 5 TRUE huber -0.4865283 0.08873101
## 6 TRUE tukey -0.4882809 0.08873266##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 319
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC -0.491 0.085 0.000 [-0.659,-0.324]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 319
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW -0.492 0.086 -0.662, -0.323 0.000 924.829
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 319
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE -0.553 0.319 -1.178, 0.071 0.083
## ------------------------------------------------------------------
WC and HT
Introduction
Title: Investigating the causality between WC on HT
- Exposure: Waist Circumference (WC), Data downloaded from: Open GWAS | Reference paper: Waist circumference 2017 | GWAS ID: ukb-a-382
- Sample size:336,639
- Ancestry: European
- Outcome: Hashimoto’s Thyroiditis (HT), Data downloaded from: GWAS catalog Database | Reference paper: Saori Sakaue 2021 | GWAS ID: GCST90018855
- Sample size:395,640 , Number of
cases:15,654 , Number of controls:
379,986
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 10,545,186 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 20,221 SNPs
3- Number of SNPs exposure after clumping : 230 SNPs
4- Number of total SNPs in outcome: 25,660,792 SNPs
5- Number of common variants between exposure and outcome: 217 SNPs
7- Number of SNPs after harmonization (action=2) = 209 SNPs
8- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 209 SNP
9- Number of SNPs after removing those that have MAF < 0.01 = 209 SNPs
10- Checking pleiotropy by PhenoScanner:
How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 29.76 34.94 42.15 54.60 54.22 660.76How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 3BmkaS MNE7VH outcome exposure MR Egger 208
## 2 3BmkaS MNE7VH outcome exposure Weighted median 208
## 3 3BmkaS MNE7VH outcome exposure Inverse variance weighted 208
## 4 3BmkaS MNE7VH outcome exposure Simple mode 208
## 5 3BmkaS MNE7VH outcome exposure Weighted mode 208
## b se pval
## 1 0.7300481 0.24080256 2.743720e-03
## 2 0.5039815 0.12500218 5.535555e-05
## 3 0.5017159 0.07837754 1.540882e-10
## 4 0.3932087 0.32459676 2.271324e-01
## 5 0.5257821 0.21480440 1.520918e-02
## id.exposure id.outcome outcome exposure method Q
## 1 3BmkaS MNE7VH outcome exposure MR Egger 237.0435
## 2 3BmkaS MNE7VH outcome exposure Inverse variance weighted 238.2007
## Q_df Q_pval
## 1 206 0.06796049
## 2 207 0.06746991## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 3BmkaS MNE7VH outcome exposure -0.004416888 0.004404478 0.3171253
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 0.5020184 0.07837133 6.405638
## 2 beta.exposure Outlier-corrected NA NA NA
## P-value
## 1 9.818503e-10
## 2 NA
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 241.5028
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.076Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 0.5020712 0.07838038 6.405572 1.498070e-10
## Iterative 0.5020712 0.07838038 6.405572 1.498070e-10
## Exact (FE) 0.5128747 0.07323148 7.003474 2.496930e-12
## Exact (RE) 0.5114683 0.07743077 6.605492 3.253484e-10
##
##
## Residual standard error: 1.07 on 208 degrees of freedom
##
## F-statistic: 41.03 on 1 and 208 DF, p-value: 9.82e-10
## Q-Statistic for heterogeneity: 238.3229 on 208 DF , p-value: 0.07320178
##
## Outliers detected
## Number of iterations = 2## SNP Q_statistic p.value
## 1 rs7752202 15.58768 7.876623e-05## id.exposure id.outcome outcome exposure method nsnp
## 1 3BmkaS MNE7VH outcome exposure MR Egger 207
## 2 3BmkaS MNE7VH outcome exposure Weighted median 207
## 3 3BmkaS MNE7VH outcome exposure Inverse variance weighted 207
## 4 3BmkaS MNE7VH outcome exposure Simple mode 207
## 5 3BmkaS MNE7VH outcome exposure Weighted mode 207
## b se pval
## 1 0.7299790 0.24150166 2.825171e-03
## 2 0.5040355 0.12857250 8.845944e-05
## 3 0.5020521 0.07873958 1.816449e-10
## 4 0.3988461 0.32952495 2.275251e-01
## 5 0.5316594 0.20897035 1.168626e-02
## id.exposure id.outcome outcome exposure method Q
## 1 3BmkaS MNE7VH outcome exposure MR Egger 237.0434
## 2 3BmkaS MNE7VH outcome exposure Inverse variance weighted 238.1959
## Q_df Q_pval
## 1 205 0.06185731
## 2 206 0.06144110## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 3BmkaS MNE7VH outcome exposure -0.004414606 0.004421923 0.3192889
Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points.
It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.
## 19 45 78 79 99 125 167
## 0.01880721 0.13144838 0.03711985 0.04752450 0.10103700 0.07282368 0.03294219
## 181 183 184 186
## 0.04406035 0.07552836 0.25576172 0.03932365## [1] 19 45 78 99 183 184 186Run After deleting new outlier: Final Results:
## id.exposure id.outcome outcome exposure method nsnp
## 1 3BmkaS MNE7VH outcome exposure MR Egger 180
## 2 3BmkaS MNE7VH outcome exposure Weighted median 180
## 3 3BmkaS MNE7VH outcome exposure Inverse variance weighted 180
## 4 3BmkaS MNE7VH outcome exposure Simple mode 180
## 5 3BmkaS MNE7VH outcome exposure Weighted mode 180
## b se pval
## 1 0.6174493 0.24939859 1.423045e-02
## 2 0.5034938 0.13046699 1.137743e-04
## 3 0.4361701 0.07962666 4.309154e-08
## 4 0.3931622 0.29682868 1.870115e-01
## 5 0.5046827 0.20982052 1.717767e-02
## id.exposure id.outcome outcome exposure method Q
## 1 3BmkaS MNE7VH outcome exposure MR Egger 120.7383
## 2 3BmkaS MNE7VH outcome exposure Inverse variance weighted 121.3266
## Q_df Q_pval
## 1 178 0.9996669
## 2 179 0.9996858## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 3BmkaS MNE7VH outcome exposure -0.003396271 0.004427943 0.4440924
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 3BmkaS MNE7VH outcome exposure MR Egger 180
## 2 3BmkaS MNE7VH outcome exposure Weighted median 180
## 3 3BmkaS MNE7VH outcome exposure Inverse variance weighted 180
## 4 3BmkaS MNE7VH outcome exposure Simple mode 180
## 5 3BmkaS MNE7VH outcome exposure Weighted mode 180
## b se pval lo_ci up_ci or or_lci95
## 1 0.6174493 0.24939859 1.423045e-02 0.1286280 1.1062705 1.854192 1.1372670
## 2 0.5034938 0.13226360 1.408075e-04 0.2442572 0.7627305 1.654492 1.2766726
## 3 0.4361701 0.07962666 4.309154e-08 0.2801018 0.5922383 1.546772 1.3232646
## 4 0.3931622 0.29260241 1.807546e-01 -0.1803385 0.9666630 1.481659 0.8349875
## 5 0.5046827 0.21261668 1.867135e-02 0.0879540 0.9214114 1.656460 1.0919379
## or_uci95
## 1 3.023063
## 2 2.144123
## 3 1.808031
## 4 2.629156
## 5 2.512834Sensitivity analyses with MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 181
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.437 0.080 0.280, 0.593 0.000
## ------------------------------------------------------------------
## Residual standard error = 0.825
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 122.4505 on 180 degrees of freedom, (p-value = 0.9997). I^2 = 0.0%.
## F statistic = 53.1.## Method Estimate Std Error 95% CI P-value
## Simple median 0.428 0.116 0.200 0.656 0.000
## Weighted median 0.504 0.132 0.245 0.762 0.000
## Penalized weighted median 0.504 0.132 0.245 0.762 0.000
##
## IVW 0.437 0.080 0.280 0.593 0.000
## Penalized IVW 0.437 0.080 0.280 0.593 0.000
## Robust IVW 0.436 0.071 0.297 0.574 0.000
## Penalized robust IVW 0.436 0.071 0.297 0.574 0.000
##
## MR-Egger 0.617 0.249 0.128 1.106 0.013
## (intercept) -0.003 0.004 -0.012 0.005 0.446
## Penalized MR-Egger 0.617 0.249 0.128 1.106 0.013
## (intercept) -0.003 0.004 -0.012 0.005 0.446
## Robust MR-Egger 0.608 0.135 0.343 0.874 0.000
## (intercept) -0.003 0.003 -0.009 0.003 0.272
## Penalized robust MR-Egger 0.608 0.135 0.343 0.874 0.000
## (intercept) -0.003 0.003 -0.009 0.003 0.272
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| 3BmkaS | MNE7VH | exposure | outcome | 0.0285585 | 0.0003855 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
Working with MRraps
## $beta.hat
## [1] 0.4422249
##
## $beta.se
## [1] 0.08155251
##
## $beta.p.value
## [1] 5.874535e-08
##
## $naive.se
## [1] 0.08077311
##
## $chi.sq.test
## [1] 122.0577## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 0.4422249 0.08155251
## 2 FALSE huber 0.4368941 0.08366440
## 3 FALSE tukey 0.4416286 0.08367047
## 4 TRUE l2 0.4422247 0.08155846
## 5 TRUE huber 0.4368941 0.08366994
## 6 TRUE tukey 0.4416286 0.08367634##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 181
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.442 0.080 0.000 [0.285,0.599]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 181
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.445 0.081 0.286, 0.604 0.000 701.373
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 181
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.521 0.162 0.204, 0.839 0.001
## ------------------------------------------------------------------
HT and BMI
Introduction
Title: Investigating the causality between HT on BMI
- Exposure: Hashimoto’s Thyroiditis (HT), Data downloaded from: GWAS catalog Database | Reference paper: Saori Sakaue 2021 | GWAS ID: GCST90018855
- Sample size:395,640 , Number of
cases:15,654 , Number of controls:
379,986
- Ancestry: European
- Outcome: Body Mass Index (BMI), Data downloaded from: GIANT consortium | Reference paper: Loic Yengo 2018 | GWAS ID: GCST006900
- Sample size: 456,426
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 25,494,034 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-5}\):: 14,295 SNPs
3- Number of SNPs exposure after clumping : 179 SNPs
4- Number of total SNPs in outcome: 2,336,260 SNPs
5- Number of common variants between exposure and outcome: 53 SNPs
6- Number of SNPs after harmonization (action=2) = 52 SNPs
7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 52 SNP
8- Number of SNPs after removing those that have MAF < 0.01 = 52 SNPs
9- Checking pleiotropy by PhenoScanner:
How many SNPs have been eliminated after checking the PhenoScanner website: 1 SNPs (rs3184504 was removed)
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 16.55 17.29 18.50 23.50 21.35 199.85How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL oJgXlR outcome exposure MR Egger 51
## 2 6R73uL oJgXlR outcome exposure Weighted median 51
## 3 6R73uL oJgXlR outcome exposure Inverse variance weighted 51
## 4 6R73uL oJgXlR outcome exposure Simple mode 51
## 5 6R73uL oJgXlR outcome exposure Weighted mode 51
## b se pval
## 1 0.005478878 0.010640670 0.6089381
## 2 -0.006486471 0.004935638 0.1887751
## 3 0.002561625 0.004707526 0.5863346
## 4 -0.003191037 0.010075860 0.7527889
## 5 -0.004636483 0.005970222 0.4410524
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL oJgXlR outcome exposure MR Egger 134.8623
## 2 6R73uL oJgXlR outcome exposure Inverse variance weighted 135.1207
## Q_df Q_pval
## 1 49 5.943739e-10
## 2 50 9.210749e-10## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 6R73uL oJgXlR outcome exposure -0.0003504132 0.001143668 0.7606027
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 0.002561625 0.004707526 0.5441553
## 2 beta.exposure Outlier-corrected -0.001297099 0.004051173 -0.3201785
## P-value
## 1 0.5887531
## 2 0.7502521
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 140.2525
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<1e-04"
##
##
## $`MR-PRESSO results`$`Outlier Test`
## RSSobs Pvalue
## 1 2.176164e-05 0.6324
## 2 3.967156e-05 0.5865
## 3 7.078166e-05 1
## 4 1.823882e-05 1
## 5 2.240769e-07 1
## 6 3.457734e-06 1
## 7 1.357282e-07 1
## 8 2.822947e-07 1
## 9 1.129529e-07 1
## 10 6.675012e-07 1
## 11 1.327403e-06 1
## 12 2.694478e-05 1
## 13 2.555663e-05 0.5049
## 14 2.476527e-05 0.4131
## 15 8.306996e-08 1
## 16 1.057478e-06 1
## 17 1.799852e-07 1
## 18 3.858341e-06 1
## 19 1.398902e-05 1
## 20 2.423330e-05 1
## 21 1.583632e-05 1
## 22 3.281091e-04 0.0051
## 23 3.130348e-06 1
## 24 1.058779e-08 1
## 25 1.470182e-04 <0.0051
## 26 1.340232e-05 1
## 27 3.466707e-05 0.1887
## 28 5.917350e-05 1
## 29 9.684654e-06 1
## 30 1.737656e-06 1
## 31 3.343801e-06 1
## 32 1.207671e-05 1
## 33 9.241574e-06 1
## 34 5.956373e-06 1
## 35 4.444152e-06 1
## 36 5.833958e-06 1
## 37 1.518520e-04 1
## 38 2.978362e-06 1
## 39 2.823519e-07 1
## 40 1.713875e-06 1
## 41 9.829770e-06 1
## 42 4.657619e-07 1
## 43 1.484710e-05 1
## 44 3.482018e-05 1
## 45 5.215603e-05 <0.0051
## 46 3.455497e-07 1
## 47 1.767064e-08 1
## 48 3.328779e-04 0.102
## 49 1.133907e-05 1
## 50 4.964850e-06 1
## 51 1.048428e-06 1
##
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 22 25 45
##
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure
## 297.4888
##
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.1394## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL oJgXlR outcome exposure MR Egger 48
## 2 6R73uL oJgXlR outcome exposure Weighted median 48
## 3 6R73uL oJgXlR outcome exposure Inverse variance weighted 48
## 4 6R73uL oJgXlR outcome exposure Simple mode 48
## 5 6R73uL oJgXlR outcome exposure Weighted mode 48
## b se pval
## 1 0.003772427 0.009092627 0.6801521
## 2 -0.006518382 0.004899026 0.1833383
## 3 -0.001297099 0.004051173 0.7488330
## 4 -0.002995373 0.010321049 0.7729247
## 5 -0.005015259 0.005798345 0.3914614
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL oJgXlR outcome exposure MR Egger 89.61718
## 2 6R73uL oJgXlR outcome exposure Inverse variance weighted 90.37526
## Q_df Q_pval
## 1 46 0.0001249282
## 2 47 0.0001468992## id.exposure id.outcome outcome exposure egger_intercept se
## 1 6R73uL oJgXlR outcome exposure -0.0006114995 0.0009802972
## pval
## 1 0.5358468
Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) -0.001297311 0.004051304 -0.3202205 0.7488012
## Iterative -0.001297311 0.004051304 -0.3202205 0.7488012
## Exact (FE) -0.001406333 0.002921940 -0.4813012 0.6303025
## Exact (RE) -0.001368682 0.004215002 -0.3247168 0.7468364
##
##
## Residual standard error: 1.387 on 47 degrees of freedom
##
## F-statistic: 0.1 on 1 and 47 DF, p-value: 0.75
## Q-Statistic for heterogeneity: 90.35764 on 47 DF , p-value: 0.000147575
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points.
It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.
## 26 35 45
## 0.3483251 0.4241893 2.4966278## [1] 3 35 45Run After deleting new outlier: Final Results:
## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL oJgXlR outcome exposure MR Egger 36
## 2 6R73uL oJgXlR outcome exposure Weighted median 36
## 3 6R73uL oJgXlR outcome exposure Inverse variance weighted 36
## 4 6R73uL oJgXlR outcome exposure Simple mode 36
## 5 6R73uL oJgXlR outcome exposure Weighted mode 36
## b se pval
## 1 -0.006751707 0.012084552 0.58002401
## 2 -0.007676646 0.005608408 0.17106977
## 3 -0.008930918 0.003691611 0.01555269
## 4 -0.002309960 0.009986617 0.81842434
## 5 -0.005702722 0.008029400 0.48226719
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL oJgXlR outcome exposure MR Egger 36.48178
## 2 6R73uL oJgXlR outcome exposure Inverse variance weighted 36.52037
## Q_df Q_pval
## 1 34 0.3540488
## 2 35 0.3979494## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 6R73uL oJgXlR outcome exposure -0.000214724 0.001132153 0.8507034
Sensitivity analyses with MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 36
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW -0.009 0.004 -0.016, -0.002 0.016
## ------------------------------------------------------------------
## Residual standard error = 1.021
## Heterogeneity test statistic (Cochran's Q) = 36.5204 on 35 degrees of freedom, (p-value = 0.3979). I^2 = 4.2%.
## F statistic = 20.3.## Method Estimate Std Error 95% CI P-value
## Simple median -0.007 0.005 -0.017 0.004 0.193
## Weighted median -0.008 0.006 -0.019 0.004 0.177
## Penalized weighted median -0.008 0.006 -0.019 0.004 0.183
##
## IVW -0.009 0.004 -0.016 -0.002 0.016
## Penalized IVW -0.009 0.004 -0.016 -0.002 0.016
## Robust IVW -0.008 0.003 -0.015 -0.001 0.017
## Penalized robust IVW -0.008 0.003 -0.015 -0.001 0.017
##
## MR-Egger -0.007 0.012 -0.030 0.017 0.576
## (intercept) 0.000 0.001 -0.002 0.002 0.850
## Penalized MR-Egger -0.007 0.012 -0.030 0.017 0.576
## (intercept) 0.000 0.001 -0.002 0.002 0.850
## Robust MR-Egger -0.005 0.007 -0.019 0.008 0.429
## (intercept) 0.000 0.001 -0.002 0.001 0.702
## Penalized robust MR-Egger -0.005 0.007 -0.019 0.008 0.429
## (intercept) 0.000 0.001 -0.002 0.001 0.702
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| 6R73uL | oJgXlR | exposure | outcome | 0.0018481 | 9.34e-05 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
Working with MRraps
## $beta.hat
## [1] -0.009356963
##
## $beta.se
## [1] 0.003839895
##
## $beta.p.value
## [1] 0.01481886
##
## $naive.se
## [1] 0.003743696
##
## $chi.sq.test
## [1] 36.23195## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 -0.009356963 0.003839895
## 2 FALSE huber -0.008720771 0.003932553
## 3 FALSE tukey -0.008645906 0.003931756
## 4 TRUE l2 -0.009355925 0.003845568
## 5 TRUE huber -0.008712942 0.003935069
## 6 TRUE tukey -0.008647392 0.003934428##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 36
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC -0.009 0.004 0.013 [-0.017,-0.002]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 36
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW -0.009 0.004 -0.017, -0.002 0.014 115.867
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 36
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE -0.006 0.007 -0.020, 0.009 0.433
## ------------------------------------------------------------------
HT and WHR
Introduction
Title: Investigating the causality between HT on WHR
- Exposure: Hashimoto’s Thyroiditis (HT), Data downloaded from: GWAS catalog Database | Reference paper: Saori Sakaue 2021 | GWAS ID: GCST90018855
- Sample size:395,640 , Number of
cases:15,654 , Number of controls:
379,986
- Ancestry: European
- Outcome: Waist to Hip Ratio (WHR), Data downloaded from: GIANT consortium | Reference paper: Dmitry Shungin 2015 | GWAS ID: GCST004064
- Sample size:142,762
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 25,494,034 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-5}\): 14,295 SNPs
3- Number of SNPs exposure after clumping : 179 SNPs
4- Number of total SNPs in outcome: 2,560,781 SNPs
5- Number of common variants between exposure and outcome: 58 SNPs
6- Number of SNPs after harmonization (action=2) = 57 SNPs
7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 57 SNP
8- Number of SNPs after removing those that have MAF < 0.01 = 57 SNPs
9- Checking pleiotropy by PhenoScanner:
How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 16.55 17.29 18.65 24.76 22.23 199.85How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL so70k9 outcome exposure MR Egger 57
## 2 6R73uL so70k9 outcome exposure Weighted median 57
## 3 6R73uL so70k9 outcome exposure Inverse variance weighted 57
## 4 6R73uL so70k9 outcome exposure Simple mode 57
## 5 6R73uL so70k9 outcome exposure Weighted mode 57
## b se pval
## 1 0.006727232 0.014697405 0.6489599
## 2 -0.003899528 0.009693418 0.6874734
## 3 -0.001203778 0.006551602 0.8542191
## 4 0.011411625 0.018440798 0.5385409
## 5 -0.003863494 0.010958315 0.7257398
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL so70k9 outcome exposure MR Egger 61.58845
## 2 6R73uL so70k9 outcome exposure Inverse variance weighted 61.99655
## Q_df Q_pval
## 1 55 0.2521533
## 2 56 0.2709054## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 6R73uL so70k9 outcome exposure -0.0009761701 0.001617016 0.5485341
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw -0.001203778 0.006551602 -0.1837379
## 2 beta.exposure Outlier-corrected NA NA NA
## P-value
## 1 0.8548827
## 2 NA
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 63.93178
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.3Studentized residuals:
Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) -0.001203861 0.006551651 -0.1837492 0.8542102
## Iterative -0.001203861 0.006551651 -0.1837492 0.8542102
## Exact (FE) -0.001254362 0.006226827 -0.2014448 0.8403508
## Exact (RE) -0.001265589 0.006854806 -0.1846280 0.8541878
##
##
## Residual standard error: 1.052 on 56 degrees of freedom
##
## F-statistic: 0.03 on 1 and 56 DF, p-value: 0.855
## Q-Statistic for heterogeneity: 61.9951 on 56 DF , p-value: 0.2709476
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points.
It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.
## 5 12 39 46
## 0.07693315 0.10001636 0.12225943 0.14141363## [1] 5 23 28 46 52Run After deleting new outlier: Final Results:
## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL so70k9 outcome exposure MR Egger 39
## 2 6R73uL so70k9 outcome exposure Weighted median 39
## 3 6R73uL so70k9 outcome exposure Inverse variance weighted 39
## 4 6R73uL so70k9 outcome exposure Simple mode 39
## 5 6R73uL so70k9 outcome exposure Weighted mode 39
## b se pval
## 1 0.01447472 0.019861103 0.47071360
## 2 0.01370317 0.012039403 0.25503985
## 3 0.01818502 0.008278459 0.02804421
## 4 0.01947715 0.021896753 0.37933133
## 5 0.01375097 0.016154081 0.39996963
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL so70k9 outcome exposure MR Egger 13.59590
## 2 6R73uL so70k9 outcome exposure Inverse variance weighted 13.63813
## Q_df Q_pval
## 1 37 0.9998470
## 2 38 0.9999066## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 6R73uL so70k9 outcome exposure 0.0004219058 0.002052908 0.8382954
Sensitivity analyses with MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 39
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.018 0.008 0.002, 0.034 0.028
## ------------------------------------------------------------------
## Residual standard error = 0.599
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 13.6381 on 38 degrees of freedom, (p-value = 0.9999). I^2 = 0.0%.
## F statistic = 20.3.## Method Estimate Std Error 95% CI P-value
## Simple median 0.022 0.012 -0.001 0.045 0.065
## Weighted median 0.015 0.012 -0.009 0.039 0.222
## Penalized weighted median 0.015 0.012 -0.009 0.039 0.222
##
## IVW 0.018 0.008 0.002 0.034 0.028
## Penalized IVW 0.018 0.008 0.002 0.034 0.028
## Robust IVW 0.018 0.008 0.002 0.035 0.027
## Penalized robust IVW 0.018 0.008 0.002 0.035 0.027
##
## MR-Egger 0.014 0.020 -0.024 0.053 0.466
## (intercept) 0.000 0.002 -0.004 0.004 0.837
## Penalized MR-Egger 0.014 0.020 -0.024 0.053 0.466
## (intercept) 0.000 0.002 -0.004 0.004 0.837
## Robust MR-Egger 0.017 0.022 -0.026 0.061 0.438
## (intercept) 0.000 0.002 -0.004 0.004 0.951
## Penalized robust MR-Egger 0.017 0.022 -0.026 0.061 0.438
## (intercept) 0.000 0.002 -0.004 0.004 0.951
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| 6R73uL | so70k9 | exposure | outcome | 0.0020064 | 0.0001279 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
Working with MRraps
## $beta.hat
## [1] 0.01857792
##
## $beta.se
## [1] 0.008931523
##
## $beta.p.value
## [1] 0.03752191
##
## $naive.se
## [1] 0.008703363
##
## $chi.sq.test
## [1] 13.54942## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 0.01857792 0.008931523
## 2 FALSE huber 0.01883015 0.009166148
## 3 FALSE tukey 0.01867057 0.009164514
## 4 TRUE l2 0.01857807 0.008937414
## 5 TRUE huber 0.01883031 0.009171609
## 6 TRUE tukey 0.01867156 0.009170091##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 39
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.019 0.008 0.028 [0.002,0.035]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 39
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.019 0.009 0.002, 0.036 0.029 120.766
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 39
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.014 0.013 -0.013, 0.040 0.305
## ------------------------------------------------------------------
HT and BFP
Introduction
Title: Investigating the causality between HT on BFP
- Exposure: Hashimoto’s Thyroiditis (HT), Data downloaded from: GWAS catalog Database | Reference paper: Saori Sakaue 2021 | GWAS ID: GCST90018855
- Sample size:395,640 , Number of
cases:15,654 , Number of controls:
379,986
- Ancestry: European
- Outcome: Body Fit Percentage (BFP), Data downloaded from: Open GWAS | Reference paper: Body fat percentage 2018 | GWAS ID: ukb-b-8909
- Sample size:454,633
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 25,494,034 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-5}\): 14,295 SNPs
3- Number of SNPs exposure after clumping : 179 SNPs
4- Number of total SNPs in outcome: 9,837,128 SNPs
5- Number of common variants between exposure and outcome: 174 SNPs
6- Number of SNPs after harmonization (action=2) = 171 SNPs
7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 170 SNP
8- Number of SNPs after removing those that have MAF < 0.01 = 170 SNPs
9- Checking pleiotropy by PhenoScanner:
How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 16.46 17.35 18.50 23.55 20.83 199.85How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL H7ku4J outcome exposure MR Egger 170
## 2 6R73uL H7ku4J outcome exposure Weighted median 170
## 3 6R73uL H7ku4J outcome exposure Inverse variance weighted 170
## 4 6R73uL H7ku4J outcome exposure Simple mode 170
## 5 6R73uL H7ku4J outcome exposure Weighted mode 170
## b se pval
## 1 -0.0013975025 0.002596241 0.5910967
## 2 0.0013232251 0.002024215 0.5133066
## 3 -0.0009193387 0.001705339 0.5898216
## 4 0.0029282555 0.004129605 0.4792466
## 5 0.0020707490 0.001720001 0.2303027
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL H7ku4J outcome exposure MR Egger 415.1483
## 2 6R73uL H7ku4J outcome exposure Inverse variance weighted 415.2963
## Q_df Q_pval
## 1 168 6.316287e-23
## 2 169 9.548802e-23## id.exposure id.outcome outcome exposure egger_intercept se
## 1 6R73uL H7ku4J outcome exposure 9.889651e-05 0.0004040262
## pval
## 1 0.8069275
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw -0.0009193387 0.001705339 -0.5390945
## 2 beta.exposure Outlier-corrected 0.0004747984 0.001557938 0.3047607
## P-value
## 1 0.5905311
## 2 0.7609348
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 420.1567
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<5e-05"
##
##
## $`MR-PRESSO results`$`Outlier Test`
## RSSobs Pvalue
## 1 2.993968e-06 1
## 2 3.223111e-05 1
## 3 4.002378e-05 1
## 4 1.722641e-09 1
## 5 9.302219e-08 1
## 6 6.915705e-06 1
## 7 5.104750e-07 1
## 8 2.665580e-05 0.918
## 9 4.663404e-05 1
## 10 2.541573e-06 1
## 11 1.376828e-06 1
## 12 1.710315e-06 1
## 13 1.223640e-05 1
## 14 6.941038e-06 1
## 15 1.342163e-06 1
## 16 7.348622e-06 1
## 17 4.859750e-05 1
## 18 7.057936e-05 1
## 19 1.615943e-10 1
## 20 2.903026e-07 1
## 21 8.853423e-08 1
## 22 9.228169e-07 1
## 23 1.436251e-05 1
## 24 8.371351e-05 1
## 25 7.019588e-05 0.6715
## 26 1.651028e-05 1
## 27 9.712558e-06 1
## 28 1.230300e-05 1
## 29 6.773404e-06 1
## 30 3.987884e-05 1
## 31 1.481176e-06 1
## 32 7.336443e-07 1
## 33 1.276333e-05 1
## 34 2.730236e-04 1
## 35 2.402538e-06 1
## 36 3.103574e-07 1
## 37 2.722363e-05 0.1445
## 38 1.871629e-07 1
## 39 5.615570e-07 1
## 40 2.559324e-06 1
## 41 4.579748e-07 1
## 42 4.896427e-06 1
## 43 1.700648e-07 1
## 44 4.679496e-06 1
## 45 3.442357e-06 1
## 46 2.374991e-05 0.6715
## 48 2.440696e-07 1
## 49 1.599876e-05 1
## 50 3.627748e-06 1
## 51 2.308251e-05 1
## 52 2.430817e-05 1
## 53 2.530929e-06 1
## 54 1.893233e-04 1
## 55 2.677875e-05 1
## 56 1.077165e-04 1
## 57 4.767320e-06 1
## 58 4.291139e-05 1
## 59 2.795432e-05 1
## 60 3.750534e-06 1
## 61 6.889389e-06 1
## 62 3.930673e-05 1
## 63 5.472017e-05 1
## 64 1.147280e-04 1
## 65 8.763319e-05 1
## 66 4.318159e-05 1
## 67 4.474650e-07 1
## 68 5.076759e-07 1
## 69 1.406887e-05 1
## 70 1.710061e-06 1
## 71 2.117642e-05 1
## 72 1.796520e-06 1
## 73 3.285509e-05 0.119
## 74 6.133388e-06 1
## 75 9.724229e-05 1
## 76 1.247020e-04 1
## 77 5.149732e-06 1
## 78 2.477891e-08 1
## 79 4.648037e-05 0.102
## 80 2.151342e-07 1
## 81 1.604179e-05 1
## 82 4.213302e-05 1
## 83 1.594964e-07 1
## 84 1.195735e-05 1
## 85 2.422739e-07 1
## 86 6.625862e-06 1
## 87 3.836948e-07 1
## 88 2.007719e-05 0.629
## 89 1.817835e-07 1
## 90 1.993733e-07 1
## 91 1.369355e-05 1
## 92 1.486756e-05 1
## 93 7.355240e-08 1
## 94 2.431221e-05 1
## 95 4.401070e-07 1
## 96 7.760977e-06 1
## 97 2.111315e-05 0.5355
## 98 4.744243e-07 1
## 99 1.638029e-07 1
## 100 6.261488e-05 1
## 101 6.225098e-06 1
## 102 5.075939e-08 1
## 103 4.134598e-05 1
## 104 4.424728e-05 1
## 105 3.384630e-09 1
## 106 2.135825e-06 1
## 107 1.060340e-05 1
## 108 2.578466e-06 1
## 109 4.789620e-09 1
## 110 1.582819e-05 1
## 111 3.536323e-06 1
## 112 4.816191e-06 1
## 113 9.664179e-07 1
## 114 2.962571e-07 1
## 115 6.132967e-06 1
## 116 1.787221e-06 1
## 117 2.249929e-05 1
## 118 9.334738e-08 1
## 119 3.537698e-04 <0.0085
## 120 5.553294e-06 1
## 121 4.405861e-06 1
## 122 5.647194e-05 1
## 123 1.047782e-05 1
## 124 7.769589e-07 1
## 125 1.195450e-05 1
## 126 3.759240e-07 1
## 127 3.685785e-05 0.68
## 128 4.821198e-06 1
## 129 1.302976e-06 1
## 130 4.494270e-06 1
## 131 3.194921e-08 1
## 132 8.968590e-07 1
## 133 2.283821e-05 1
## 134 1.991849e-06 1
## 135 2.469714e-06 1
## 136 3.156653e-08 1
## 137 1.506738e-07 1
## 138 2.405914e-05 1
## 139 1.496503e-05 1
## 140 5.775510e-06 1
## 141 6.396838e-07 1
## 142 5.081249e-05 1
## 143 9.795254e-06 1
## 144 2.756790e-06 1
## 145 1.581839e-04 1
## 146 3.943027e-06 1
## 147 1.260562e-04 1
## 148 2.520379e-06 1
## 149 4.369437e-04 <0.0085
## 150 7.267053e-05 0.3485
## 151 7.946165e-05 0.068
## 152 1.558277e-04 <0.0085
## 153 4.910289e-06 1
## 154 8.791249e-07 1
## 155 6.746693e-07 1
## 156 2.182593e-06 1
## 157 1.182095e-05 1
## 158 2.698137e-04 1
## 159 8.379539e-06 1
## 160 1.929714e-04 <0.0085
## 161 1.467221e-06 1
## 162 2.931246e-05 1
## 163 1.104821e-06 1
## 164 3.581255e-07 1
## 165 6.750336e-06 1
## 166 4.416109e-05 <0.0085
## 167 2.209820e-06 1
## 168 6.475971e-06 1
## 169 3.994662e-07 1
## 170 4.861213e-06 1
## 171 3.136828e-07 1
##
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 118 148 151 159 165
##
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure
## -293.6272
##
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.15685## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL H7ku4J outcome exposure MR Egger 165
## 2 6R73uL H7ku4J outcome exposure Weighted median 165
## 3 6R73uL H7ku4J outcome exposure Inverse variance weighted 165
## 4 6R73uL H7ku4J outcome exposure Simple mode 165
## 5 6R73uL H7ku4J outcome exposure Weighted mode 165
## b se pval
## 1 0.0001946182 0.002350816 0.9341221
## 2 0.0013464596 0.001943286 0.4883863
## 3 0.0004747984 0.001557938 0.7605484
## 4 0.0032381756 0.004064939 0.4268287
## 5 0.0019749158 0.001729258 0.2550938
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL H7ku4J outcome exposure MR Egger 319.9986
## 2 6R73uL H7ku4J outcome exposure Inverse variance weighted 320.0485
## Q_df Q_pval
## 1 163 2.722104e-12
## 2 164 3.795524e-12## id.exposure id.outcome outcome exposure egger_intercept se
## 1 6R73uL H7ku4J outcome exposure 5.752233e-05 0.0003605807
## pval
## 1 0.8734512
Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 0.0004742166 0.001558239 0.3043284 0.7608777
## Iterative 0.0004742166 0.001558239 0.3043284 0.7608777
## Exact (FE) 0.0004894686 0.001115481 0.4387962 0.6608092
## Exact (RE) 0.0004846189 0.001418492 0.3416437 0.7330564
##
##
## Residual standard error: 1.397 on 164 degrees of freedom
##
## F-statistic: 0.09 on 1 and 164 DF, p-value: 0.761
## Q-Statistic for heterogeneity: 320.0367 on 164 DF , p-value: 3.806746e-12
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points.
It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.
## [1] 24 34 53 55 64 74 75 143 145 154Run After deleting new outlier: Final Results:
## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL H7ku4J outcome exposure MR Egger 134
## 2 6R73uL H7ku4J outcome exposure Weighted median 134
## 3 6R73uL H7ku4J outcome exposure Inverse variance weighted 134
## 4 6R73uL H7ku4J outcome exposure Simple mode 134
## 5 6R73uL H7ku4J outcome exposure Weighted mode 134
## b se pval
## 1 0.001418850 0.001848012 0.44399428
## 2 0.002254136 0.001923568 0.24125657
## 3 0.003045252 0.001258795 0.01555548
## 4 0.003730695 0.004271566 0.38403078
## 5 0.001754246 0.001741085 0.31549596
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL H7ku4J outcome exposure MR Egger 152.8676
## 2 6R73uL H7ku4J outcome exposure Inverse variance weighted 154.5363
## Q_df Q_pval
## 1 132 0.10333141
## 2 133 0.09755242## id.exposure id.outcome outcome exposure egger_intercept se
## 1 6R73uL H7ku4J outcome exposure 0.0003421534 0.0002850413
## pval
## 1 0.2321476
Sensitivity analyses with MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 134
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.003 0.001 0.001, 0.006 0.016
## ------------------------------------------------------------------
## Residual standard error = 1.078
## Heterogeneity test statistic (Cochran's Q) = 154.5363 on 133 degrees of freedom, (p-value = 0.0976). I^2 = 13.9%.
## F statistic = 23.5.## Method Estimate Std Error 95% CI P-value
## Simple median 0.003 0.002 -0.001 0.007 0.134
## Weighted median 0.002 0.002 -0.001 0.006 0.232
## Penalized weighted median 0.002 0.002 -0.002 0.006 0.347
##
## IVW 0.003 0.001 0.001 0.006 0.016
## Penalized IVW 0.003 0.001 0.000 0.005 0.024
## Robust IVW 0.002 0.001 0.000 0.004 0.044
## Penalized robust IVW 0.002 0.001 0.000 0.004 0.042
##
## MR-Egger 0.001 0.002 -0.002 0.005 0.443
## (intercept) 0.000 0.000 0.000 0.001 0.230
## Penalized MR-Egger 0.002 0.002 -0.002 0.005 0.367
## (intercept) 0.000 0.000 0.000 0.001 0.341
## Robust MR-Egger 0.002 0.001 0.000 0.004 0.139
## (intercept) 0.000 0.000 0.000 0.001 0.631
## Penalized robust MR-Egger 0.002 0.001 0.000 0.004 0.130
## (intercept) 0.000 0.000 0.000 0.001 0.642
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| 6R73uL | H7ku4J | exposure | outcome | 0.0079555 | 0.0003548 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
Working with MRraps
## $beta.hat
## [1] 0.003206916
##
## $beta.se
## [1] 0.001250331
##
## $beta.p.value
## [1] 0.01032194
##
## $naive.se
## [1] 0.001219894
##
## $chi.sq.test
## [1] 154.2275## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 0.003206916 0.001250331
## 2 FALSE huber 0.002206292 0.001270191
## 3 FALSE tukey 0.002253920 0.001270698
## 4 TRUE l2 0.003204189 0.001252717
## 5 TRUE huber 0.002212728 0.001270962
## 6 TRUE tukey 0.002261531 0.001271542##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 134
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.003 0.001 0.010 [0.001,0.006]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 134
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.003 0.001 0.001, 0.006 0.015 260.463
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 134
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.002 0.002 -0.002, 0.005 0.302
## ------------------------------------------------------------------
HT and WC
Introduction
Title: Investigating the causality between HT on WC
- Exposure: Hashimoto’s Thyroiditis (HT), Data downloaded from: GWAS catalog Database | Reference paper: Saori Sakaue 2021 | GWAS ID: GCST90018855
- Sample size:395,640 , Number of
cases:15,654 , Number of controls:
379,986
- Ancestry: European
- Outcome: Waist Circumference (WC), Data downloaded from: Open GWAS | Reference paper: Waist circumference 2017 | GWAS ID: ukb-a-382
- Sample size:336,639
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 25,494,034 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-5}\): 14,295 SNPs
3- Number of SNPs exposure after clumping : 179 SNPs
4- Number of total SNPs in outcome: 10,545,186 SNPs
5- Number of common variants between exposure and outcome: 168 SNPs
6- Number of SNPs after harmonization (action=2) = 165 SNPs
7- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 162 SNP
8- Number of SNPs after removing those that have MAF < 0.01 = 162 SNPs
9- Checking pleiotropy by PhenoScanner:
How many SNPs have been eliminated after checking the PhenoScanner website: 1 SNPs (rs76121445 was removed)
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 16.46 17.39 18.51 23.71 20.86 199.85How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL 7BHc6A outcome exposure MR Egger 161
## 2 6R73uL 7BHc6A outcome exposure Weighted median 161
## 3 6R73uL 7BHc6A outcome exposure Inverse variance weighted 161
## 4 6R73uL 7BHc6A outcome exposure Simple mode 161
## 5 6R73uL 7BHc6A outcome exposure Weighted mode 161
## b se pval
## 1 -0.002210156 0.003312126 0.5055528
## 2 -0.001641161 0.003114782 0.5982670
## 3 0.003327312 0.002221375 0.1341692
## 4 -0.001873353 0.007171434 0.7942554
## 5 -0.002424260 0.002569686 0.3468952
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL 7BHc6A outcome exposure MR Egger 318.3255
## 2 6R73uL 7BHc6A outcome exposure Inverse variance weighted 328.2986
## Q_df Q_pval
## 1 159 1.021194e-12
## 2 160 1.105737e-13## id.exposure id.outcome outcome exposure egger_intercept se
## 1 6R73uL 7BHc6A outcome exposure 0.001140525 0.0005110046
## pval
## 1 0.02701746
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 0.003327312 0.002221375 1.497862
## 2 beta.exposure Outlier-corrected 0.003351006 0.002154507 1.555347
## P-value
## 1 0.1361394
## 2 0.1218642
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 333.0604
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<4e-05"
##
##
## $`MR-PRESSO results`$`Outlier Test`
## RSSobs Pvalue
## 1 1.083801e-06 1
## 2 3.523556e-05 1
## 3 1.303273e-04 1
## 4 1.063530e-06 1
## 5 3.080596e-06 1
## 6 4.148264e-06 1
## 7 8.715192e-07 1
## 8 2.413899e-05 1
## 9 7.620106e-05 1
## 10 1.059277e-06 1
## 11 3.741748e-07 1
## 12 2.138889e-05 1
## 13 1.947290e-05 1
## 14 5.833383e-06 1
## 15 6.555700e-06 1
## 16 2.518988e-06 1
## 17 1.782016e-04 1
## 18 9.742534e-04 1
## 19 3.667826e-08 1
## 20 2.175583e-05 1
## 21 1.663309e-05 1
## 22 4.556503e-08 1
## 23 8.023767e-06 1
## 24 9.767583e-05 1
## 25 6.803576e-05 1
## 26 1.152534e-09 1
## 27 2.366667e-05 1
## 28 4.570747e-05 0.3542
## 29 1.427864e-05 1
## 30 1.242892e-05 1
## 31 2.991978e-06 1
## 32 4.213713e-08 1
## 33 3.284766e-05 1
## 34 3.615531e-04 1
## 35 1.519815e-07 1
## 36 1.921884e-07 1
## 37 2.337238e-05 1
## 38 8.845814e-06 1
## 39 4.886524e-06 1
## 40 1.735210e-05 1
## 41 1.977244e-05 1
## 42 7.547959e-06 1
## 43 1.408294e-08 1
## 44 1.512739e-07 1
## 45 9.015672e-06 1
## 46 2.459540e-05 1
## 48 1.249408e-06 1
## 49 4.020778e-06 1
## 50 1.244066e-07 1
## 51 2.035851e-05 1
## 52 1.937992e-03 1
## 53 3.288365e-06 1
## 54 6.768536e-06 1
## 55 1.525007e-04 1
## 56 1.095689e-05 1
## 57 8.440530e-07 1
## 58 1.687917e-06 1
## 59 1.664257e-04 1
## 60 2.353381e-04 1
## 61 1.508197e-04 1
## 62 1.581029e-04 1
## 63 7.082876e-04 1
## 64 3.011190e-06 1
## 65 9.747415e-07 1
## 66 2.793201e-05 1
## 67 8.775126e-07 1
## 68 3.306591e-06 1
## 69 3.114949e-05 1
## 70 1.306202e-05 1
## 71 2.440744e-06 1
## 72 5.583718e-05 0.25116
## 73 1.549755e-05 1
## 74 9.014785e-04 0.09016
## 75 2.185922e-04 1
## 76 9.623372e-05 1
## 77 1.708361e-07 1
## 78 6.796791e-05 0.43148
## 79 7.883293e-07 1
## 80 6.376698e-06 1
## 81 1.875865e-04 0.13524
## 82 4.627589e-10 1
## 83 1.050435e-05 1
## 84 5.660097e-09 1
## 85 6.191976e-08 1
## 86 1.238448e-05 1
## 87 6.628403e-07 1
## 88 3.223876e-06 1
## 89 2.535464e-06 1
## 90 5.273577e-05 1
## 91 4.210885e-08 1
## 92 1.609539e-05 1
## 93 3.399226e-07 1
## 94 2.918507e-06 1
## 95 5.819685e-07 1
## 96 1.932479e-05 1
## 97 2.724513e-06 1
## 98 5.380784e-10 1
## 99 3.490462e-04 1
## 100 1.927300e-06 1
## 101 3.924309e-05 0.40572
## 102 1.480927e-05 1
## 103 4.093293e-05 1
## 104 9.851894e-06 1
## 105 1.370135e-05 1
## 106 5.741842e-05 1
## 107 4.276537e-06 1
## 108 8.245868e-07 1
## 109 6.940826e-05 1
## 110 6.579292e-06 1
## 111 2.411837e-08 1
## 112 2.014650e-06 1
## 113 8.704087e-07 1
## 114 1.896175e-07 1
## 115 2.566534e-05 1
## 116 3.934184e-06 1
## 117 3.997442e-04 0.0322
## 118 1.483805e-05 1
## 119 3.029389e-06 1
## 120 4.599248e-07 1
## 121 2.910009e-05 1
## 122 1.745002e-04 0.32844
## 123 5.265811e-05 1
## 124 2.380212e-05 1
## 125 2.213171e-05 1
## 126 5.082176e-06 1
## 127 8.652006e-05 1
## 128 1.042280e-05 1
## 129 3.566747e-06 1
## 130 1.971190e-06 1
## 131 2.348087e-05 1
## 132 1.368100e-05 1
## 133 5.230015e-06 1
## 134 6.155218e-08 1
## 136 3.643073e-05 1
## 137 2.939079e-05 1
## 138 4.982820e-09 1
## 139 6.849058e-05 1
## 140 3.937192e-06 1
## 141 5.189563e-06 1
## 142 1.952222e-04 1
## 143 3.640331e-07 1
## 144 2.039154e-04 1
## 145 2.868000e-05 1
## 146 9.655415e-05 1
## 147 8.247561e-05 1
## 149 6.241155e-06 1
## 150 3.860011e-06 1
## 151 4.063901e-05 1
## 152 8.231531e-07 1
## 153 3.345050e-05 1
## 154 2.089742e-04 1
## 155 2.878644e-04 0.04508
## 156 5.586490e-06 1
## 157 2.411955e-05 1
## 158 3.293509e-08 1
## 159 1.467490e-05 1
## 160 8.829188e-06 1
## 162 9.302383e-05 1
## 163 8.149381e-07 1
## 164 6.747971e-06 1
## 165 7.936025e-07 1
##
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 116 152
##
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure
## -0.7070675
##
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.99132## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL 7BHc6A outcome exposure MR Egger 159
## 2 6R73uL 7BHc6A outcome exposure Weighted median 159
## 3 6R73uL 7BHc6A outcome exposure Inverse variance weighted 159
## 4 6R73uL 7BHc6A outcome exposure Simple mode 159
## 5 6R73uL 7BHc6A outcome exposure Weighted mode 159
## b se pval
## 1 -0.002021410 0.003198106 0.5282640
## 2 -0.001641042 0.003157126 0.6032101
## 3 0.003491301 0.002150272 0.1044493
## 4 -0.001673982 0.007545969 0.8247266
## 5 -0.002177075 0.002583624 0.4007013
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL 7BHc6A outcome exposure MR Egger 291.9129
## 2 6R73uL 7BHc6A outcome exposure Inverse variance weighted 301.7794
## Q_df Q_pval
## 1 157 3.581292e-10
## 2 158 4.579940e-11## id.exposure id.outcome outcome exposure egger_intercept se
## 1 6R73uL 7BHc6A outcome exposure 0.001134486 0.0004924854
## pval
## 1 0.02255727
Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 0.003553541 0.002160589 1.644710 0.10002971
## Iterative 0.003553541 0.002160589 1.644710 0.10002971
## Exact (FE) 0.003952520 0.001566989 2.522366 0.01165682
## Exact (RE) 0.003707247 0.002651300 1.398275 0.16399018
##
##
## Residual standard error: 1.381 on 158 degrees of freedom
##
## F-statistic: 2.71 on 1 and 158 DF, p-value: 0.102
## Q-Statistic for heterogeneity: 301.2983 on 158 DF , p-value: 5.152118e-11
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points.
It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.
Run After deleting new outlier: Final Results:
## id.exposure id.outcome outcome exposure method nsnp
## 1 6R73uL 7BHc6A outcome exposure MR Egger 125
## 2 6R73uL 7BHc6A outcome exposure Weighted median 125
## 3 6R73uL 7BHc6A outcome exposure Inverse variance weighted 125
## 4 6R73uL 7BHc6A outcome exposure Simple mode 125
## 5 6R73uL 7BHc6A outcome exposure Weighted mode 125
## b se pval
## 1 1.183682e-02 0.005196701 2.446742e-02
## 2 6.700444e-03 0.003958383 9.050826e-02
## 3 1.312719e-02 0.002407227 4.945930e-08
## 4 -3.720637e-06 0.010190699 9.997093e-01
## 5 3.059193e-03 0.007136228 6.688964e-01
## id.exposure id.outcome outcome exposure method Q
## 1 6R73uL 7BHc6A outcome exposure MR Egger 121.1337
## 2 6R73uL 7BHc6A outcome exposure Inverse variance weighted 121.2122
## Q_df Q_pval
## 1 123 0.5306974
## 2 124 0.5540659## id.exposure id.outcome outcome exposure egger_intercept se
## 1 6R73uL 7BHc6A outcome exposure 0.0001626082 0.0005803708
## pval
## 1 0.7798101
Sensitivity analyses with MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 125
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.013 0.002 0.008, 0.018 0.000
## ------------------------------------------------------------------
## Residual standard error = 0.989
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 121.2122 on 124 degrees of freedom, (p-value = 0.5541). I^2 = 0.0%.
## F statistic = 20.1.## Method Estimate Std Error 95% CI P-value
## Simple median 0.007 0.004 0.000 0.014 0.065
## Weighted median 0.009 0.004 0.001 0.017 0.033
## Penalized weighted median 0.008 0.004 0.000 0.016 0.039
##
## IVW 0.013 0.002 0.008 0.018 0.000
## Penalized IVW 0.013 0.002 0.008 0.018 0.000
## Robust IVW 0.012 0.003 0.007 0.017 0.000
## Penalized robust IVW 0.012 0.003 0.007 0.017 0.000
##
## MR-Egger 0.012 0.005 0.002 0.022 0.023
## (intercept) 0.000 0.001 -0.001 0.001 0.779
## Penalized MR-Egger 0.012 0.005 0.002 0.022 0.023
## (intercept) 0.000 0.001 -0.001 0.001 0.779
## Robust MR-Egger 0.011 0.005 0.001 0.021 0.034
## (intercept) 0.000 0.001 -0.001 0.001 0.776
## Penalized robust MR-Egger 0.011 0.005 0.001 0.021 0.034
## (intercept) 0.000 0.001 -0.001 0.001 0.776
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| 6R73uL | 7BHc6A | exposure | outcome | 0.0063675 | 0.0004484 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
Working with MRraps
## $beta.hat
## [1] 0.01379663
##
## $beta.se
## [1] 0.00256772
##
## $beta.p.value
## [1] 7.739192e-08
##
## $naive.se
## [1] 0.002503808
##
## $chi.sq.test
## [1] 119.7756## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 0.01379663 0.002567720
## 2 FALSE huber 0.01308101 0.002629427
## 3 FALSE tukey 0.01294610 0.002628516
## 4 TRUE l2 0.01379606 0.002571626
## 5 TRUE huber 0.01310340 0.002673050
## 6 TRUE tukey 0.01295295 0.002662056##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 125
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.014 0.003 0.000 [0.009,0.019]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 125
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.014 0.003 0.009, 0.019 0.000 214.094
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 125
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.003 0.007 -0.011, 0.017 0.662
## ------------------------------------------------------------------
Multivariable MR
Checking weakness of the instruments:
##
## Conditional F-statistics for instrument strength
##
## exposure1 exposure2 exposure3
## F-statistic 62.89468 42.04917 70.12359How many SNPs have been eliminated with checking the weakness: 0 SNP
initial IVW-MVMR:
##
## Multivariable MR
##
## Estimate Std. Error t value Pr(>|t|)
## exposure1 0.17763275 0.1899744 0.9350351 0.36039864
## exposure2 0.08922646 0.1919340 0.4648810 0.64680086
## exposure3 0.45932468 0.2084595 2.2034241 0.03886521
##
## Residual standard error: 0.944 on 21 degrees of freedom
##
## F-statistic: 1.83 on 3 and 21 DF, p-value: 0.172
##
## ------------------------------
## Q-Statistics for instrument strength:
##
## exposure1 exposure2 exposure3
## Q 1509.472 1009.18 1682.966
##
## ------------------------------
## Q-Statistic for instrument validity:
##
## 18.66954 on 20 DF , p-value: 0.5433899initial Egger-MVMR:
##
## Multivariable MR-Egger method
## (variants uncorrelated, random-effect model)
##
## Orientated to exposure : 1
## Number of Variants : 24
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure_1 0.298 0.489 -0.661, 1.257 0.542
## exposure_2 0.077 0.208 -0.332, 0.485 0.713
## exposure_3 0.456 0.221 0.022, 0.889 0.039
## (intercept) -0.002 0.009 -0.019, 0.015 0.787
## ------------------------------------------------------------------
## Residual standard error = 0.966
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic = 18.6538 on 20 degrees of freedom, (p-value = 0.5444)pleiotropy MVMR test
## Q-Statistic for instrument validity:
## 18.66954 on 20 DF , p-value: 0.5433899Testing Outlier with Radial test
##
## Radial Multivariable MR
##
## Estimate Std. Error t value Pr(>|t|)
## exposure1 0.17763275 0.1899744 0.9350351 0.36039864
## exposure2 0.08922646 0.1919340 0.4648810 0.64680086
## exposure3 0.45932468 0.2084595 2.2034241 0.03886521
##
## Residual standard error: 0.944 on 21 degrees of freedom## snp wj corrected_beta qj qj_p ref_exposure
## 1 rs10245306 0.6012270 0.365023862 0.021112344 0.88447332 Exposure_1
## 2 rs10938397 0.6900585 -0.095682225 0.051548109 0.82039102 Exposure_1
## 3 rs11165643 0.5916230 -0.546195534 0.309967507 0.57770012 Exposure_1
## 4 rs11538 0.5892857 3.490799048 6.468631088 0.01097951 Exposure_1
## 5 rs12881629 1.3006135 -0.104882179 0.103808054 0.74730681 Exposure_1
## 6 rs13107325 0.4912281 -0.292436186 0.108544113 0.74180777 Exposure_1
## 7 rs13174863 0.6596859 0.520861675 0.077715017 0.78041817 Exposure_1
## 8 rs1421334 0.6666667 -1.954076029 3.029454869 0.08176548 Exposure_1
## 9 rs1503526 2.1840491 -0.031958752 0.095942210 0.75675458 Exposure_1
## 10 rs1884389 0.8421053 -1.099481102 1.373490344 0.24121310 Exposure_1
## 11 rs2237403 1.3874346 0.564257768 0.207392200 0.64881909 Exposure_1
## 12 rs2307111 0.5238095 -2.410850896 3.509653490 0.06101222 Exposure_1
## 13 rs3754963 0.8711656 0.946464646 0.514948181 0.47300464 Exposure_1
## 14 rs3803286 1.0584795 0.841980693 0.467168614 0.49429263 Exposure_1
## 15 rs429343 1.2146597 0.931269123 0.689887574 0.40620262 Exposure_1
## 16 rs4482463 0.6845238 -1.496726863 1.919048881 0.16596155 Exposure_1
## 17 rs4722398 2.0306748 0.068221904 0.024308665 0.87610210 Exposure_1
## 18 rs543874 0.9239766 -0.051108594 0.048344859 0.82596878 Exposure_1
## 19 rs7124681 1.0785340 0.259645857 0.007254382 0.93212413 Exposure_1
## 20 rs7206608 0.7857143 2.386694686 3.834250084 0.05021545 Exposure_1
## 21 rs7498665 0.9079755 0.322885291 0.019156740 0.88991807 Exposure_1
## 22 rs8027205 0.5263158 -1.529725300 1.534248158 0.21547599 Exposure_1
## 23 rs9304665 1.0471204 -0.508355962 0.492754459 0.48270117 Exposure_1
## 24 rs9367368 0.9047619 1.476836532 1.527175193 0.21653689 Exposure_1
## 25 rs10245306 0.6129466 -0.094581708 0.020708673 0.88557542 Exposure_2
## 26 rs10938397 0.6597018 0.375118248 0.053920138 0.81637716 Exposure_2
## 27 rs11165643 0.6377382 0.760714341 0.287553595 0.59179253 Exposure_2
## 28 rs11538 0.6498750 -2.915046007 5.865546284 0.01544007 Exposure_2
## 29 rs12881629 1.3545337 -0.182042326 0.099675743 0.75221910 Exposure_2
## 30 rs13107325 0.6645439 0.436699470 0.080235359 0.77697871 Exposure_2
## 31 rs13174863 0.8916492 0.343164072 0.057497385 0.81049607 Exposure_2
## 32 rs1421334 0.6163036 2.395134214 3.277015862 0.07025656 Exposure_2
## 33 rs1503526 1.9335460 -0.147518937 0.108372128 0.74200511 Exposure_2
## 34 rs1884389 0.8091754 -1.239860215 1.429385263 0.23186479 Exposure_2
## 35 rs2237403 1.2861204 0.506307868 0.223729521 0.63621279 Exposure_2
## 36 rs2307111 0.7278929 -1.773509753 2.525632592 0.11200985 Exposure_2
## 37 rs3754963 0.8709202 -0.679822072 0.515093278 0.47294229 Exposure_2
## 38 rs3803286 0.9734035 0.811638797 0.507999418 0.47600618 Exposure_2
## 39 rs429343 1.4648691 -0.535683790 0.572050170 0.44944538 Exposure_2
## 40 rs4482463 0.7287500 1.661972970 1.802586141 0.17940016 Exposure_2
## 41 rs4722398 1.7669080 0.214970331 0.027937502 0.86725584 Exposure_2
## 42 rs543874 1.0799064 0.284939387 0.041364249 0.83883645 Exposure_2
## 43 rs7124681 0.9221623 -0.006693672 0.008484513 0.92660952 Exposure_2
## 44 rs7206608 0.7777560 2.320892472 3.873483780 0.04905460 Exposure_2
## 45 rs7498665 0.7009325 -0.098931090 0.024815299 0.87482817 Exposure_2
## 46 rs8027205 0.5343813 1.770815096 1.511091520 0.21897261 Exposure_2
## 47 rs9304665 0.9519215 -0.665366024 0.542033429 0.46159123 Exposure_2
## 48 rs9367368 0.9107976 1.379820625 1.517054840 0.21806573 Exposure_2
## 49 rs10245306 0.5628736 0.659484343 0.022550908 0.88063081 Exposure_3
## 50 rs10938397 1.1795088 0.619224557 0.030157648 0.86213301 Exposure_3
## 51 rs11165643 0.7683874 1.016639209 0.238660745 0.62517507 Exposure_3
## 52 rs11538 0.7237262 -2.238382822 5.267008354 0.02173333 Exposure_3
## 53 rs12881629 0.8877423 0.873231631 0.152087100 0.69654878 Exposure_3
## 54 rs13107325 1.8932456 0.337358960 0.028163232 0.86672564 Exposure_3
## 55 rs13174863 0.6745131 0.795008705 0.076006676 0.78278381 Exposure_3
## 56 rs1421334 0.6726369 2.572112679 3.002565820 0.08313276 Exposure_3
## 57 rs1503526 0.6979571 -0.196529601 0.300222620 0.58374289 Exposure_3
## 58 rs1884389 0.4071462 -2.182144893 2.840806203 0.09189809 Exposure_3
## 59 rs2237403 0.3584445 -1.037188480 0.802754968 0.37027095 Exposure_3
## 60 rs2307111 1.0206012 1.787828303 1.801281382 0.17955766 Exposure_3
## 61 rs3754963 0.7043067 -0.491652918 0.636945712 0.42481897 Exposure_3
## 62 rs3803286 0.6779649 -0.577895231 0.729371693 0.39308692 Exposure_3
## 63 rs429343 0.5823455 -1.112614398 1.438971456 0.23030585 Exposure_3
## 64 rs4482463 1.2564048 1.371561761 1.045550519 0.30653407 Exposure_3
## 65 rs4722398 0.8799755 0.711806542 0.056095877 0.81277651 Exposure_3
## 66 rs543874 1.7639942 0.339510419 0.025322941 0.87356501 Exposure_3
## 67 rs7124681 1.1652513 0.535234421 0.006714515 0.93469272 Exposure_3
## 68 rs7206608 0.6052143 -2.408571151 4.977782477 0.02567487 Exposure_3
## 69 rs7498665 1.4237055 0.366689124 0.012217309 0.91198752 Exposure_3
## 70 rs8027205 0.4052316 -1.758196232 1.992685350 0.15806039 Exposure_3
## 71 rs9304665 0.6218063 1.614528159 0.829797431 0.36233111 Exposure_3
## 72 rs9367368 0.5425661 2.625825961 2.546657466 0.11052787 Exposure_3## q_statistic p_value
## Exposure_1 26.43581 0.1903168
## Exposure_2 24.97327 0.2483238
## Exposure_3 28.86038 0.1173941
Run After deleting new outlier:
##
## Multivariable MR
##
## Estimate Std. Error t value Pr(>|t|)
## exposure1 0.1079069 0.1512116 0.7136154 0.484615866
## exposure2 0.1271972 0.1557161 0.8168531 0.424692259
## exposure3 0.5016454 0.1702701 2.9461747 0.008637962
##
## Residual standard error: 0.74 on 18 degrees of freedom
##
## F-statistic: 3.31 on 3 and 18 DF, p-value: 0.0436
##
## ------------------------------
## Q-Statistics for instrument strength:
##
## exposure1 exposure2 exposure3
## Q 1478.424 926.7414 1535.57
##
## ------------------------------
## Q-Statistic for instrument validity:
##
## 9.825719 on 17 DF , p-value: 0.9107591##
## Multivariable MR-Egger method
## (variants uncorrelated, random-effect model)
##
## Orientated to exposure : 1
## Number of Variants : 21
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure_1 0.471 0.526 -0.559, 1.501 0.370
## exposure_2 0.078 0.220 -0.354, 0.510 0.723
## exposure_3 0.514 0.231 0.062, 0.967 0.026
## (intercept) -0.007 0.010 -0.027, 0.012 0.454
## ------------------------------------------------------------------
## Residual standard error = 0.739
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic = 9.2963 on 17 degrees of freedom, (p-value = 0.9305)## Q-Statistic for instrument validity:
## 9.825719 on 17 DF , p-value: 0.9107591Sensitivity analyses with MendelianRandomization Package
##
## Multivariable inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 21
##
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure_1 0.108 0.204 -0.293, 0.508 0.597
## exposure_2 0.127 0.210 -0.285, 0.540 0.546
## exposure_3 0.502 0.230 0.051, 0.953 0.029
## ------------------------------------------------------------------
## Residual standard error = 0.740
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic = 9.8581 on 18 degrees of freedom, (p-value = 0.9364)##
## Multivariable MR-Egger method
## (variants uncorrelated, random-effect model)
##
## Orientated to exposure : 1
## Number of Variants : 21
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure_1 0.471 0.526 -0.559, 1.501 0.370
## exposure_2 0.078 0.220 -0.354, 0.510 0.723
## exposure_3 0.514 0.231 0.062, 0.967 0.026
## (intercept) -0.007 0.010 -0.027, 0.012 0.454
## ------------------------------------------------------------------
## Residual standard error = 0.739
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic = 9.2963 on 17 degrees of freedom, (p-value = 0.9305)